tag:blogger.com,1999:blog-33852808019505631722024-02-20T23:41:16.157-08:00300 EXERCICIS (explicats i resolts)els problemes, si són matemàtics, no són tan greusjoan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.comBlogger358125tag:blogger.com,1999:blog-3385280801950563172.post-48919480856637346282023-01-01T00:17:00.003-08:002023-04-29T23:29:59.712-07:00MÀGIA NADALENCA BÀSICA<p> <span style="font-family: Helvetica; font-size: 15px; text-align: justify;">(Un mag fa aquest joc a un programa de radio)</span></p><p style="font-family: Helvetica; font-size: 15px; font-stretch: normal; line-height: normal; margin: 0px; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none;">Col·locau les cinc peces fonamentals del betlem de forma que el nin Jesús quedi al mig, als seus costats la Verge i Sant Josep, i en els extrems el bou i la mula</span></p><p style="font-family: Helvetica; font-size: 15px; font-stretch: normal; line-height: normal; margin: 0px; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none;">Per exemple:</span></p><p style="color: #20a603; font-family: Helvetica; font-size: 20px; font-stretch: normal; line-height: normal; margin: 0px; text-align: center;"><span style="-webkit-font-kerning: none; font-kerning: none;">MVNJB</span></p><p style="color: #118dff; font-family: Helvetica; font-size: 20px; font-stretch: normal; line-height: normal; margin: 0px; text-align: center;"><span style="-webkit-font-kerning: none; font-kerning: none;">BVNJM</span></p><p style="color: #fb9e09; font-family: Helvetica; font-size: 20px; font-stretch: normal; line-height: normal; margin: 0px; text-align: center;"><span style="-webkit-font-kerning: none; font-kerning: none;">BJNVM</span></p><p style="font-family: Helvetica; font-size: 15px; font-stretch: normal; line-height: normal; margin: 0px; min-height: 18px;"><span style="text-align: justify;">Mourem el nin Jesús. Heu de seguir les meves instruccions.Cada moviment és un intercanvi de posició del nin anb una de les peces que tengui al costat. </span><span style="-webkit-font-kerning: none; font-kerning: none;"></span></p><p style="font-family: Helvetica; font-size: 15px; font-stretch: normal; line-height: normal; margin: 0px; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none;">Pot canviar a dreta o esquerra (si està en un extrem la direcció serà obligada)</span></p><p style="font-family: Helvetica; font-size: 15px; font-stretch: normal; line-height: normal; margin: 0px; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none;">Començam:</span></p><p style="font-family: Helvetica; font-size: 15px; font-stretch: normal; line-height: normal; margin: 0px; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none;"><span class="Apple-tab-span" style="white-space: pre;"> </span>1) El nin Jesús fa un moviment</span></p><p style="font-family: Helvetica; font-size: 15px; font-stretch: normal; line-height: normal; margin: 0px; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none;"><span class="Apple-tab-span" style="white-space: pre;"> </span>2) Ara podeu moure el nin tantes vegades com volgueu (sempre seguint les regles esmentades a dalt). Suposem N moviments</span></p><p style="font-family: Helvetica; font-size: 15px; font-stretch: normal; line-height: normal; margin: 0px; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none;"><span class="Apple-tab-span" style="white-space: pre;"> </span>3) M’ha agradat. Tornau fer N moviments</span></p><p style="font-family: Helvetica; font-size: 15px; font-stretch: normal; line-height: normal; margin: 0px; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none;"><span class="Apple-tab-span" style="white-space: pre;"> </span>4) Estic segur d’una cosa: Ningú té el nin a un cap de la formació. Podeu eliminar els dos elements que estan en els extrems i ningú farà el paper d’Herodes</span></p><p style="font-family: Helvetica; font-size: 15px; font-stretch: normal; line-height: normal; margin: 0px; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none;"><span class="Apple-tab-span" style="white-space: pre;"> </span>5) Per acabar feu un darrer moviment, el que us doni la gana</span></p><p style="font-family: Helvetica; font-size: 15px; font-stretch: normal; line-height: normal; margin: 0px; min-height: 18px; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none;"></span><br /></p><p style="font-family: Helvetica; font-size: 15px; font-stretch: normal; line-height: normal; margin: 0px; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none;">Ara puc endevinar on és el nin Jesús: TOTS TENIU EL NIN JESÚS ALTRE COP AL MIG !!!</span></p><p style="font-family: Helvetica; font-size: 15px; font-stretch: normal; line-height: normal; margin: 0px; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none;"><br /></span></p><p style="font-family: Helvetica; font-size: 15px; font-stretch: normal; line-height: normal; margin: 0px; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none;">(Amb això i un poc de teatre ja pots exercir de Mag amateur. Però, quin és el fonament del joc?)</span></p><div><span style="-webkit-font-kerning: none; font-kerning: none;"><br /></span></div><div><span style="-webkit-font-kerning: none; font-kerning: none; font-size: large;">Si necessites ajuda clica <a href="https://drive.google.com/file/d/1LXYpCfqrxUa0Ah86VCS4Y2u6Cz2kw7G9/view?usp=sharing ">AQUÍ</a></span></div>joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-40290033188780591492019-05-22T22:59:00.002-07:002023-04-29T08:32:38.058-07:00PROBLEMA 300 + 50<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Helvetica Neue"; font-size: 15px; font-stretch: normal; line-height: normal; text-align: justify;">
<span style="-webkit-font-kerning: none; font-kerning: none;">Tres amics decideixen jugar a póquer amb fitxes. Comencen amb 1998, 2998 i 3998 fitxes respectivament. Un d’ells proposa les següents regles: “A cada jugada tots apostarem el mateix nombre de fitxes, al manco una; la quantitat la decidirà el que en aquell moment sigui més pobre (en fitxes)”.</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;">Un altre demana: “ I què farem si els dos més pobres tenen la mateixa quantitat de fitxes, què passa aleshores?</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;">El primer respon: “Això no passarà ,és impossible”.</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;">Com n’està tan segur?</span></div>
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<tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/17XfSK8J6iHYEqDZpZFLNnzCyfE41iq36/view?usp=sharing"><img border="0" data-original-height="75" data-original-width="100" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipw1gha-2JQ1PEApHBxlQyS1ZyysowYYwCsT_rS_twwl1Y7tmEkIDti19EB0ouD_eSzINug5tsxyRQCSE9GvAXdD3Izx7XGtu_j1yvKIu0vaAC0QZvBTi0N4tffRulpci9Kfo3WZlEuXg/s1600/portanova42bmp.bmp" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/17XfSK8J6iHYEqDZpZFLNnzCyfE41iq36/view?usp=sharing">AJUDA I SOLUCIÓ</a></td></tr>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-45004589728206115972019-05-15T22:46:00.001-07:002023-04-29T09:24:24.953-07:00PROBLEMA 300+49<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: Times; font-size: 14.7px; font-stretch: normal; line-height: normal; margin-bottom: 14.7px;">
<span style="-webkit-font-kerning: none; background-color: black;"><span style="color: white;">(Proves Cangur 2019 nivell 2batx)</span></span></div>
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<span style="-webkit-font-kerning: none; background-color: black;"><span style="color: white;">Del conjunt {1, 2, 3…10} n’escollim a l’atzar tres nombres diferents. Quina és la probabilitat que un dels tres sigui la mitjana dels altres dos? </span></span></div>
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<tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/1zX0gR6t_6j6-Kofikm39riHsiE_k3vm6/view?usp=sharing"><img border="0" data-original-height="100" data-original-width="75" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFdqN3DwiHaYgJiIfRSl2qp86GYQbMWAxMxTKsrSSBY0qLN6degH_i6_8V9YuvAQm-KGbBnFkSOMkvw8RV9BhZdsPfaC2J4SdmjqUQvILcPWX1ajPYpIXGRSazHjqlMBvU1NcHLjBuRGM/s1600/portanova12bmp.bmp" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1zX0gR6t_6j6-Kofikm39riHsiE_k3vm6/view?usp=sharing">AJUDA I SOLUCIÓ</a></td></tr>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-43667137948537271442019-05-14T09:54:00.003-07:002023-04-29T12:27:39.400-07:00PROBLEMA 300+48<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-size: 15px; font-stretch: normal; line-height: normal;">
<span style="-webkit-text-stroke-width: initial;">(“Alice in puzzle-land”- Raymond Smullyan)</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;">Havien robat el llibre de receptes a la Reina de Cors. El principal sospitós era la cuinera de la duquessa; de fet, el llibre va aparèixer a la cuina de la duquessa. Només hi havia tres sospitosos: la cuinera, la duquessa i el moix de Cheshire.</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;">-El llibre el va robar el moix de Cheshire!- va dir la duquessa en el judici.</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;">-Sí. Jo el vaig robar- va dir el moix amb un gran somriure.</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;">-Jo no el vaig robar! - va dir la cuinera.</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;">El lladre havia mentit i al menys un dels altres dos havia dit la veritat.</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;">Qui va robar el llibre de receptes?</span></div>
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<tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/1H9mwUqh6-oIxuBUaEeU7uPFoSeZo8fIh/view?usp=sharing"><img border="0" data-original-height="120" data-original-width="90" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVSc85E6K51MNNLZZz0P1DcUoALcy5o7e0yYtV_NBbGUf-rKQuQsNfHed4Y29nEPMBGVkcSiG6d78LD8eJbNkvj0xSXT5zxsocfzVriLYqtEF50xvHuGv66Lq_1s9gsKT7xDk_TCQI5g0/s1600/lo%25CC%2580gica1.bmp" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1H9mwUqh6-oIxuBUaEeU7uPFoSeZo8fIh/view?usp=sharing">AJUDA I SOLUCIÓ</a></td></tr>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-36685363112823031602019-05-08T09:37:00.002-07:002023-04-30T08:52:37.462-07:00PROBLEMA 300 + 47<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-size: 15px; font-stretch: normal; line-height: normal;">
<span style="-webkit-text-stroke-width: initial;">(un clàssic de Boris Kordemsky)</span></div>
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<span style="-webkit-text-stroke-width: initial; font-size: large;">Un jove ambiciós i mandrós ha convocat el diable per tal d’aconseguir fer-se ric sense gaire esforç.</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;"><span style="font-size: large;">Estan a la vora d’un riu. El diable li proposa un senzill negoci:</span></span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;"><span style="font-size: large;">-Veus aquest pont?. Si el creues et doblaré els diners que tens a la butxaca. De fet, cada vegada que el passis et doblaré els diners que tenguis.</span></span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;"><span style="font-size: large;">-Vaja!</span></span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;"><span style="font-size: large;">-Però hi ha una petita condició;jo som generós, però tu m’hauràs de donar 24 rubles després de cada traspàs.</span></span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;"><span style="font-size: large;">El jove hi consentí. Creuà el pont i comprovà que el seu capital s’havia doblat</span></span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;"><span style="font-size: large;">Va donar 24 rubles al diable i tornà ràpid a creuar el pont.</span></span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;"><span style="font-size: large;">Els diners s’havien doblat altra vegada, així que tornà pagar 24 rubles al vell diable.</span></span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;"><span style="font-size: large;">Per tercera vegada va creuar el pont i per tercera vegada doblà la quantitat de diners que tenia.</span></span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;"><span style="font-size: large;">Però , la sorpresa va ser gran, ara el jove només tenia 24 rubles. No podia fer altra cosa que pagar els 24 rubles i quedar-se amb les butxaques buides.</span></span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;"><span style="font-size: large;">Quants rubles va perdre el jove?</span></span></div>
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<tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/1eCXM-lSZCn_vY35qOxQSa1ungp899W1j/view?usp=sharing"><img border="0" data-original-height="75" data-original-width="100" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9PBXVvslWjpXB6G2FKSRpeQzRqaT7Lck_zzPfUkwPACBJT1v8WxZ7ICBP5hC7j90zcltUMjR8z2o5q3EsWl-OOThpmtLWQFHbbnJOQIQJQ_fXgGhJ8Ye_CpvKh1SCpwddqwmKkjMrzPM/s1600/portanova11bmp.bmp" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1eCXM-lSZCn_vY35qOxQSa1ungp899W1j/view?usp=sharing">AJUDA I SOLUCIÓ</a></td></tr>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-78832226337999440932019-05-04T11:11:00.019-07:002023-05-03T08:40:12.335-07:00PROBLEMA 300 + 46<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-size: 15px; font-stretch: normal; line-height: normal;"><div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-stretch: normal; line-height: normal;"><span style="-webkit-text-stroke-width: initial;">(“Alice in puzzle-land”- Raymond Smullyan)</span></div><br style="font-family: -webkit-standard;" /><div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-stretch: normal; line-height: normal; text-align: justify;"><span style="-webkit-font-kerning: none;"><span style="font-size: large;">Un home havia d’anar en bicicleta a l’estació del tren que era dotze quilòmetres lluny. Va pensar de la següent manera: “Tenc una hora i mitja de temps per arribar-hi. Quatre quilòmetres són costa amunt i hauré de fer-los a peu, a quatre per hora; hi ha quatre quilòmetres de baixada , i aquests els faré a dotze per hora; els quatre restants són plans i podré anar a vuit per hora. La mitjana és de vuit quilòmetres per hora , per tant arribaré a l’hora exacta”. És correcte el seu raonament?</span></span></div><div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-stretch: normal; line-height: normal; text-align: justify;"><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/1o_fyGYQZpdyFXmI_lTSrX83q4w4Ainlm/view?usp=sharing"><img border="0" data-original-height="79" data-original-width="67" height="79" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXTcO_FYHwh5sFYC1Z8BwF_43myiJgIhHTVy3bcCVv8xXQXuZjIkQTBTbcgRdqNSVE7O718_hUEjEGcYQrRqQ7M3EAschaYqEAq51j3rV504mep8lRy-If8jOp_OA_tEyRt63bVu74B7ppmPVOa-1bGCOq5lxMVWGsJG5RRv0-O6YNpEZ9OCaBZ1RF/s1600/fosca12.bmp" width="67" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1o_fyGYQZpdyFXmI_lTSrX83q4w4Ainlm/view?usp=sharing">ajuda i solució</a></td></tr></tbody></table></div>joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-2761454009382166812019-04-16T09:52:00.001-07:002023-05-01T07:58:24.085-07:00PROBLEMA 300 + 45<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-size: 15px; font-stretch: normal; line-height: normal; text-align: justify;">
<span style="-webkit-font-kerning: none; font-kerning: none;">(Youtube - Genial) </span></div>
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<span style="-webkit-text-stroke-width: initial;">Quatre nins estan formats en fila. Tots miren en una mateixa direcció. Una paret separa el quart dels altres tres</span><span style="-webkit-font-kerning: none; font-kerning: none;"></span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;">El primer pot veure el segon i el tercer</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;">El segon pot veure el tercer</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;">El tercer i el quart no en poden veure cap.</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;">Cada un porta una gorra del color que es veu a la figura.</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;">Se’ls informa que hi ha dues gorres vermelles i dues color de cel, però cap d’ells sap el color de la seva.</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;">No poden girar-se,ni moure’s,no poden parlar ni treure’s la gorra.</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;">Té premi el primer que cridi quin color té la seva gorra i ho faci amb la certesa d’encertar segur. </span><span style="-webkit-text-stroke-width: initial;">Qui guanyarà?</span><br />
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<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1zyzXJOVuMl_fquqSKlN3DiG1GqryXS_r/view?usp=sharing">Ajuda i solució</a></td></tr>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-26812025298348518202019-04-13T03:31:00.002-07:002023-05-02T02:34:49.686-07:00PROBLEMA 300 + 44<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-size: 15px; font-stretch: normal; line-height: normal; text-align: justify;">
<span style="-webkit-font-kerning: none; font-kerning: none;">(Revista CACUMEN no43) </span></div>
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Posau les xifres de l’1 al 8 , sense repetir-ne cap, en els cercles de la figura de forma que els vèrtexs de cada un dels quatre triangles vermells sumin el mateix, i que aquesta suma sigui la més baixa possible.<br />
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<tr><td style="text-align: center;"><span style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/1g2qqjx3wDKGjm6Q-WiS5NO7MrELmnf4F/view?usp=sharing"><img border="0" data-original-height="100" data-original-width="75" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgj3xnvOV98OAl7KS-eotjkVLlfDsvTAE2sI-uM8g4tY61tRo2ibmnCIgnB2LQUB5fYb7jBIyWzal1C4DYh0q0KJE2nVtuGKNP4_xrZA4k9ZVDByPeA5pPSovTeS4q6FsJX9WcT_1xJIg/s1600/portanova30bmp.bmp" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1g2qqjx3wDKGjm6Q-WiS5NO7MrELmnf4F/view?usp=sharing">AJUDA I SOLUCIÓ</a></td></tr>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-17957455461743453092019-04-04T23:30:00.002-07:002023-05-02T09:13:45.097-07:00PROBLEMA 300 + 43<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-stretch: normal; line-height: normal;">
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(Revista CACUMEN no.39)</div>
<span style="-webkit-text-stroke-width: initial; text-align: justify;"><span style="font-size: large;">En un congrés es parlaran sis idiomes . A part del català hi haurà el francès, l’alemany, l’anglès, l’holandès, el polonès i el galès. Una persona dotada de sentit de l’humor ha contractat sis intèrprets els llinatges dels quals són: Francès, Alemany, Anglès, Holandès, Polonès i Galès.</span></span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;"><span style="font-size: large;">Cada un d’ells parla (a més del català) dos dels sis idiomes i cada idioma és parlat per dos d’ells. Hem sabut: </span></span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;"><span style="font-size: large;">(primer) Els intèrprets Francès i Holandès parlen, entre tots dos, els quatre idiomes que no són ,justament, ni francès ni holandès. </span></span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;"><span style="font-size: large;">(segon) Els traductors que tenen per llinatges els noms dels dos idiomes parlats pel senyor Holandès parlen francès.</span></span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;"><span style="font-size: large;">(tercer) El traductor de cognom Anglès parla alemany i holandès</span></span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;"><span style="font-size: large;">(quart) Un dels seus col·legues parla holandès i polonès i cap d’ells parla alhora polonès i alemany.</span></span></div>
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<span style="-webkit-font-kerning: none;"><span style="font-size: large;">Quins dos idiomes parla Polonès ?</span></span></div>
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<tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://es.scribd.com/document/405042382/pr343pdf"><img border="0" data-original-height="120" data-original-width="104" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAP4BsuYOdogoBl8UY2l8enI7sm0G7Ts3skxuxhi9w-ZSWbn448cfYmA2LwKTkbpecJiGqZN1eesp5VXsad-fTWn0pO_Wsd3WsZgvKiOJ8fWa76hJEvHXllcPXEqVbMaDcqPavc6ODjkk/s1600/fosca10.bmp" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://es.scribd.com/document/405042382/pr343pdf">Ajuda i solució</a></td></tr>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-89181768897914954502019-04-01T08:59:00.003-07:002023-05-02T09:19:24.751-07:00PROBLEMA 300 + 42<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-size: 15px; font-stretch: normal; line-height: normal;">
<span style="-webkit-font-kerning: none; font-kerning: none;">(Revista CACUMEN no. 39)</span></div>
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<span style="-webkit-font-kerning: none;"><span style="font-size: large;">Quatre parelles joves, els Greens,Pinks,Browns i Whites, són excel·lents jugadors de tennis i han organitzat un torneig de dobles mixtes.</span></span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;"><span style="font-size: large;">Han convingut que cada persona formarà parella amb el cònjuge de cada una de les altres, contra cada una de les altres parelles formades de la mateixa manera. En cap cas els jugadors formaran parella amb el propi cònjuge.</span></span></div>
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<span style="-webkit-text-stroke-width: initial;"><span style="font-size: large;">Si juguen dos partits cada dia, quants dies durarà el torneig?</span></span></div>
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<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1-nc8wyJvZ8ZrlSiVCRFykFmvEJGgDCG4/view?usp=sharing">AJUDA I SOLUCIÓ</a></td></tr>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-23463005585237125672019-03-29T11:15:00.003-07:002023-05-02T11:54:58.609-07:00PROBLEMA 300 + 41<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-size: 15px; font-stretch: normal; line-height: normal;">
<span style="-webkit-font-kerning: none; font-kerning: none;">(“Scientific American”- Martin Gardner)</span></div>
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<span style="-webkit-font-kerning: none;"><span style="font-size: large;">Teniu tres persones davant vostre. Una contesta sempre dient la veritat, una altra sempre menteix i la tercera contesta a l’atzar, de vegades menteix i altres diu la veritat. No sabeu quina és cadascuna d’elles, però les tres es coneixen perfectament entre sí. Com podeu identificar les tres fent només tres preguntes?</span></span></div>
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<span style="-webkit-text-stroke-width: initial; font-size: large;">(Les preguntes poden adreçar-se a qualsevol dels tres i han de poder ser contestades amb un “sí” o un “no”).</span></div>
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<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1mTM4RaV0EucA8ukfLPMObFg82dxYFjiX/view?usp=sharing">AJUDA I SOLUCIÓ</a></td></tr>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-27328529909881724892019-03-20T03:24:00.016-07:002023-05-03T09:18:00.206-07:00PROBLEMA 300 + 40<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-size: 15px; font-stretch: normal; line-height: normal;"><div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-stretch: normal; line-height: normal;"><span style="-webkit-text-stroke-width: initial;">(vist a Youtube- exposició de Adrián Paenza)</span></div><div style="font-family: "book antiqua"; font-stretch: normal; line-height: normal; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none; font-size: large;">Tres amics, Aina , Biel, i Claudi, juguen un capvespre a ping-pong. S’enfronten dos d’ells en una partida i qui guanya jugarà tot seguit contra el tercer que descansava. Aquest ritme es va repetint fins al final: juguen dos i el guanyador s’enfronta al tercer que esperava. Acaba el temps de jugar i resulta que Aina ha jugat 17 partides, Biel 15 i Claudi 10 . Qui va perdre la segona partida?</span></div><div style="font-family: "book antiqua"; font-stretch: normal; line-height: normal; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none; font-size: large;"><br /></span></div></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/1Dab6QCtP6twgCGvQQkKrid8p7ifb48o9/view?usp=sharing"><img border="0" data-original-height="59" data-original-width="94" height="59" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJa49ZFN_3TvxoAWDsGGpkW5gHozdoj37M5Xi_hsR6npChUhD8hL4GQM3aRkyyWX_jW7iVV89jTHkQKhKXh6H0WcCB8toNycfaNGpr8Lre7IcXK87MGgBWcHmSM_Yu2KUr1teM_Z47fM86CUgQVW22BKHKUsXJbi1EtrFScYWaG7__VvqVjXYAF42W/s1600/fosca18.bmp" width="94" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1Dab6QCtP6twgCGvQQkKrid8p7ifb48o9/view?usp=sharing">AJUDA I SOLUCIÓ</a></td></tr></tbody></table><br /><div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-size: 15px; font-stretch: normal; line-height: normal;"><br /></div>
joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-19554922410473678082019-03-08T08:29:00.003-08:002023-05-03T22:59:38.537-07:00PROBLEMA 300 + 39<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-size: 13px; font-stretch: normal; line-height: normal; text-align: justify;">
<span style="-webkit-font-kerning: none; font-kerning: none;">Copa Cangur Internacional 2017</span></div>
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<span style="-webkit-font-kerning: none;"><span style="font-size: large;">Quants nombres de dos dígits N tenen la propietat que tres cops N és més petit que el nombre que obtens a l’intercanviar les xifres de N ?</span></span></div>
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<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/14MNJFEaEnau_fRpD7YsZcKmeE8_7AWIK/view?usp=sharing">AJUDA I SOLUCIÓ</a></td></tr>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-14219727835254943292019-02-28T10:01:00.003-08:002023-05-03T23:04:40.509-07:00PROBLEMA 300 + 38<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-size: 13px; font-stretch: normal; line-height: normal; text-align: justify;">
<span style="-webkit-font-kerning: none; font-kerning: none;">Copa Cangur Internacional 2018</span></div>
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<span style="-webkit-font-kerning: none;"><span style="font-size: large;">Mil persones seuen al voltant d’una taula rodona. Cadascuna d’elles és honesta (que sempre diu la veritat) o mentidera (que sempre menteix). Totes elles diuen: “Estic asseguda al costat d’una persona mentidera i d’una honesta”. Quantes persones mentideres hi ha a la taula?</span></span></div>
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<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1PQVMicnHFMONvjKDJ5RfrC9R-qGQNZgy/view?usp=sharing">AJUDA I SOLUCIÓ<br />
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-62440078422661002062019-02-25T23:13:00.003-08:002023-05-04T03:45:11.068-07:00PROBLEMA 300 + 37<div style="font-family: "book antiqua"; font-stretch: normal; line-height: normal; text-align: justify;">
<span style="-webkit-font-kerning: none; font-kerning: none;">IV Copa Cangur</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none; font-size: large;">Tenim sis bosses que contenen 18,19,21,23,25 i 34 boles respectivament.En cinc d’aquestes bosses totes les boles són blanques i en l’altra totes són negres. En Joan agafa tres bosses de les que tenen les boles blanques. En Jaume agafa les altres dues bosses de boles blanques. Al comptar les boles de cadascú observen que en Joan té exactament el doble de boles que en Jaume. Quantes boles té en Joan? </span><br />
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<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1wIVNG1v3cy_MvC2l_ElcjU-UjpRYrwsv/view?usp=sharing">AJUDA I SOLUCIÓ</a></td></tr>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-27990679211259546372019-02-18T09:23:00.001-08:002023-05-04T04:07:13.384-07:00PROBLEMA 300 + 36<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-size: 13px; font-stretch: normal; line-height: normal; text-align: justify;">
<span style="-webkit-font-kerning: none; font-kerning: none;">VI Copa Cangur</span></div>
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<span style="font-size: large;"><span style="-webkit-font-kerning: none;">Si simplificam la fracció 100! / 2</span><span style="-webkit-font-kerning: none; font-stretch: normal; line-height: normal;"><sup>100</sup></span><span style="-webkit-font-kerning: none;"> fins a obtenir una fracció irreductible, quin serà el denominador?</span></span></div>
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<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1S1MB2uIK6mt-TdBPjIxQU2O4B86dhFQU/view?usp=sharing">AJUDA I SOLUCIÓ</a></td></tr>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-35031489912154887472019-02-14T22:50:00.002-08:002023-05-04T04:23:08.584-07:00PROBLEMA 300 + 35<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-stretch: normal; line-height: normal; text-align: justify;">
<span style="-webkit-font-kerning: none;">(Un criptograma senzill) </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjJM_L3N_sYukeBZX4w2vJb6Gd6wtnnEab7UPH9_TnHWBQaw1JWLsBpPMJp-ULJ5PyGEvW_oDYv3hbED1x6mq3n677UQdghYp3lQ73wYL6ZntIHuBR-TaRzpFDJ5moSUKm77aXUJ19zfI/s1600/pr335i1bmp.bmp" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="160" data-original-width="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjJM_L3N_sYukeBZX4w2vJb6Gd6wtnnEab7UPH9_TnHWBQaw1JWLsBpPMJp-ULJ5PyGEvW_oDYv3hbED1x6mq3n677UQdghYp3lQ73wYL6ZntIHuBR-TaRzpFDJ5moSUKm77aXUJ19zfI/s1600/pr335i1bmp.bmp" /></a></div>
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<span style="font-size: large;"><span style="-webkit-text-stroke-width: initial;">Reconstruïu aquesta multiplicació, on les X són dígits </span><span style="-webkit-text-stroke-width: initial;">qualssevol</span></span></div>
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<tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/1mvcpU2KebiGEu6CrP-Vo2p9YtyqJtN9C/view?usp=sharing"><img border="0" data-original-height="100" data-original-width="75" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcO7WFg0ELmbp8HVS8qx03yP9nVEPL11NLqG5EH1mXQpHe3S8PtmAy1D5l6j8RtkDGHiiyEZlv3Z-4JOViPZGN0GUfA3-LmUjgkgmMV7uhNynUTFbTzFDFlTvhqQY9t6nXhZA7FIo2BDQ/s1600/portanova31bmp.bmp" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1mvcpU2KebiGEu6CrP-Vo2p9YtyqJtN9C/view?usp=sharing">AJUDA I SOLUCIÓ</a></td></tr>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-65739318988536903772019-02-10T22:06:00.003-08:002023-05-04T08:10:43.855-07:00PROBLEMA 300 + 34<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-size: 13px; font-stretch: normal; line-height: normal;">
<span style="-webkit-font-kerning: none; font-kerning: none;">VI Copa Cangur 2019</span></div>
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<span style="-webkit-font-kerning: none;"><span style="font-size: large;">El professor de matemàtiques va fer tres proves per qualificar els seus alumnes. Tots els alumnes havien de fer ,com a mínim, dues proves i n’hi va haver 12 que van fer les tres proves. Si el 70% dels alumnes van fer la primera, el 80% van fer la segona i el 90% van fer la tercera, quants alumnes hi havia a la classe?</span></span></div>
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<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1Qv0krtDo-Nuuf8NgvSVn9Y_wIR21BJag/view?usp=sharing">AJUDA I SOLUCIÓ</a></td></tr></tbody></table>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-41349361262345867762019-02-07T22:55:00.002-08:002023-05-04T10:24:57.348-07:00PROBLEMA 300 + 33<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-size: 13px; font-stretch: normal; line-height: normal;">
<span style="-webkit-font-kerning: none; font-kerning: none;">Eurocup 2016</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiILWlQMWTyBJkGymqBT-KJlvcYP4F0XfY9i9pJsTHPlmoEe8bsAOgK0JjVqc5ma1exGQLAw_Mxb2KM43W7neBIH96JU7EGwfpz4t8d8Sat878lnGO8QaMsWNsOUk7kg1MxX2rESe0zxus/s1600/pr333i1bmp.bmp" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="75" data-original-width="100" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiILWlQMWTyBJkGymqBT-KJlvcYP4F0XfY9i9pJsTHPlmoEe8bsAOgK0JjVqc5ma1exGQLAw_Mxb2KM43W7neBIH96JU7EGwfpz4t8d8Sat878lnGO8QaMsWNsOUk7kg1MxX2rESe0zxus/s1600/pr333i1bmp.bmp" /></a></div>
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<span style="-webkit-font-kerning: none;"><span style="font-size: large;">Cada lletra representa una sola xifra entre 0 i 9. Lletres diferents representen xifres diferents. Quant val la suma de les diferents sumes que es poden obtenir (és a dir, la suma dels nombres GOOD que poden ser resultat de l’operació)?</span></span></div>
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<tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/1fpyxsVtz1i5U2Vda-qFOON3gi1PSRKmf/view?usp=sharing"><img border="0" data-original-height="75" data-original-width="100" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgF3p6wtRuT8f1TAMjig0DdETURO-fcyBBMmsXHncZr60zWJxMejpkovxp8AAT7O-mSz0CWuFeoVICVRHPxYmHIrHibwHtNm-UYw248E078yp4viNt0NxPXBL5FrfzorL7ZP4IeGmqMm7s/s1600/portanova36bmp.bmp" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1fpyxsVtz1i5U2Vda-qFOON3gi1PSRKmf/view?usp=sharing">AJUDA I SOLUCIÓ</a></td></tr>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-86728430206227303842019-02-03T09:43:00.002-08:002023-05-04T23:04:50.855-07:00PROBLEMA 300 + 32<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-stretch: normal; line-height: normal; text-align: justify;">
<span style="-webkit-font-kerning: none;">V Copa Cangur 2018 (fase final catalana)</span></div>
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<span style="-webkit-font-kerning: none;"><span style="font-size: large;">La Jana va pensar un nombre de tres xifres, i quatre amigues seves van provar d’endevinar-lo, proposant els nombres 541, 837, 291 i 846. La Jana els va dir: “Cadascuna de vosaltres heu encertat exactament una de les xifres del nombre, i les quatre l’heu encertat en la posició correcta. A més, cadascuna de les xifres del nombre ha estat encertada almenys per una de vosaltres”. Quin és el nombre que va pensar la Jana?.</span></span></div>
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<tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/1bflnERtDfB88hP5KVxnnLGLFK8pyzPMR/view?usp=sharing"><img border="0" data-original-height="77" data-original-width="58" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhv8pIDMoh1J5x1biIkk2zuKnw_guS10tQlaRqlgFG1nlpYruEBSALvW9_GjV-x2TTBskI2o8BOvw6QOW-IqJmum6EpF3sTbxFUi3PFoagOHOAd9sB84HhkyBFfRp0laBv4mNrLcBAPGag/s1600/lo%25CC%2580gica2.bmp" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1bflnERtDfB88hP5KVxnnLGLFK8pyzPMR/view?usp=sharing">ajuda i solució</a></td></tr>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-29418956789109518062019-01-30T21:50:00.003-08:002023-05-04T23:27:33.376-07:00PROBLEMA 300 + 31<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-size: 13px; font-stretch: normal; line-height: normal; text-align: justify;">
<span style="-webkit-font-kerning: none; font-kerning: none;">III Copa Cangur 2016 (primera fase)</span></div>
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<span style="-webkit-font-kerning: none;"><span style="font-size: large;">A la pastisseria de la Valentina hi ha capses de galetes (més d’una). Sabem que totes les capses contenen el mateix nombre de galetes, i que hi ha més d’una galeta a cada capsa. La Valentina assegura que si ens digués el nombre exacte de galetes que hi ha en total, aleshores podríem deduir amb tota seguretat quantes capses hi ha. Si el nombre total de galetes està entre 200 i 300, quantes capses hi ha?</span></span></div><div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-stretch: normal; line-height: normal; text-align: justify;"><span style="-webkit-font-kerning: none;"><span style="font-size: large;"><br /></span></span></div>
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<tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/1L3jXC692sZ9EQbHNLIaw7g4Ot_QbspUh/view?usp=sharing"><img border="0" data-original-height="100" data-original-width="75" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisnmcR52Bwy9NAETvmXvKMRme2OR4Pvzipp894B0LF5ZSPbPoZFP055VuZpgfvI2UTYF5-5t6pqRujwLmHv3EjGqMS2m0wxQqHbXZsOI9-lpOmQmOJKtWdKWtWk6lJLAFw6MyP6dI_skw/s1600/portanova30bmp.bmp" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1L3jXC692sZ9EQbHNLIaw7g4Ot_QbspUh/view?usp=sharing">Ajuda i solució</a></td></tr>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-34728852238768648182019-01-24T02:30:00.003-08:002023-05-04T23:34:46.319-07:00PROBLEMA 300+30<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-stretch: normal; line-height: normal;">
<span style="-webkit-font-kerning: none;">Cangur Eurocup 2018</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;"><span style="font-size: large;">Hi ha 30 portes en un edifici i el bidell n’ha barrejat les 30 claus (totes diferents). En el pitjor dels casos, quantes proves haurà de fer per tal de saber a quina porta correspon cada clau?</span></span></div><div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-stretch: normal; line-height: normal; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none;"><span style="font-size: large;"><br /></span></span></div>
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<tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/1TjGU9lszrqGKTJZlGQI4n6ELiZ7v4pAQ/view?usp=sharing"><img border="0" data-original-height="75" data-original-width="100" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzKihMkDW-17NMdd3vdODjeW8t0YaDmCwdv4a65R4glhY9o9PhP7f-cHS4sSJm4b_8z9JdrF-axEqq1ISNcOmj-ms4BU0fyI1oJ5k1nLZz-Kvl-RZBP4_Ii15D0DbOh0-aPpr2ZRA25n0/s1600/portanova28bnp.bmp" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1TjGU9lszrqGKTJZlGQI4n6ELiZ7v4pAQ/view?usp=sharing">AJUDA I SOLUCIÓ</a></td></tr></tbody></table>
joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-8808675770992307422019-01-20T00:20:00.003-08:002023-05-05T03:54:42.794-07:00PROBLEMA 300 + 29<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: "Book Antiqua"; font-size: 13px; font-stretch: normal; line-height: normal; text-align: justify;">
<span style="-webkit-font-kerning: none; font-kerning: none;">Copa Cangur Catalunya 2018 </span></div>
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<span style="font-size: large;">Una pilota de futbol està formada per 12 pentàgons regulars i 20 hexàgons regulars. Els costats dels pentàgons i dels hexàgons tenen una longitud de 4’5cm.<span style="-webkit-font-kerning: none; font-kerning: none;"></span></span></div>
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<span style="font-size: large;">Quina és la longitud total de les costures que mantenen enganxats els pentàgons i els hexàgons?</span></div><div style="font-family: "book antiqua"; font-stretch: normal; line-height: normal; min-height: 16px; text-align: justify;"><span style="font-size: large;"><br /></span></div>
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<tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/10oqQGqbXPPGYzgexQUWgzRPmmT88b5-a/view?usp=sharing"><img border="0" data-original-height="91" data-original-width="90" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlPo33OqpGa52X8vnznCdtHNGiqJgbjbXvUTRBsJPJY2sUxBwHOYcjUO2X-59bE0DnahwIdsyKsEL5uQQXXiuY518Zhk3FNgfaexLigrzEkmTwMmu6esHbfx14XpHOJKgBMXBrllVXZKw/s1600/marca6.bmp" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/10oqQGqbXPPGYzgexQUWgzRPmmT88b5-a/view?usp=sharing">AJUDA I SOLUCIÓ</a></td></tr>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-24978253911457217372019-01-15T23:53:00.004-08:002023-05-05T21:26:23.306-07:00PROBLEMA 300 + 28<div style="font-family: "book antiqua"; font-stretch: normal; line-height: normal; text-align: justify;">
<div style="font-size: 12px;">LIV OME</div>
<span style="font-size: large;"><span style="-webkit-font-kerning: none;">Sigui n un nombre natural. Provar que si l’última xifra de 7</span><span style="-webkit-font-kerning: none; font-stretch: normal; line-height: normal;"><sup>n</sup></span><span style="-webkit-font-kerning: none;"> és 3, la penúltima és 4.</span></span></div>
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<tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/1ZA62sIEUP9B8aqivok4Mzctj_FWaR6tt/view?usp=sharing"><img border="0" data-original-height="66" data-original-width="108" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUMrkEyw2ZhOLt2uRnc5WV6tn-h_vBe1cRFQ3HG4iRKXzKUZFLSr189Cp_wdMkXA-ahGyfE0vU1qULmpeIyWJ5J27Nr5j_FPBHRjHND1WQJ_D1CXVlPvPjsKcZI36FFkLOdtus-nBXuf8/s1600/fosca8.bmp" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/1ZA62sIEUP9B8aqivok4Mzctj_FWaR6tt/view?usp=sharing">AJUDA I SOLUCIÓ</a><div style="text-align: left;">
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0tag:blogger.com,1999:blog-3385280801950563172.post-56467152976088048782019-01-10T23:15:00.005-08:002023-05-05T21:34:06.439-07:00PROBLEMA 300 + 27<div style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: Times; font-size: 16px; font-stretch: normal; line-height: normal;">
<span style="-webkit-font-kerning: none; font-kerning: none;">Proves Cangur 1999</span></div>
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<span style="-webkit-font-kerning: none; font-kerning: none;">Una illa és habitada per persones honrades,que sempre diuen la veritat, i per mentiders,que sempre menteixen. Hi ha 1999 persones a l’illa. A cada una d’elles li agrada o bé cantar, o bé jugar a futbol, o bé pescar, però només una d’aquestes activitats. Un dia es va fer una enquesta a cada habitant de l’illa que consistia en tres preguntes:</span></div>
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<li style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: Times; font-size: 16px; font-stretch: normal; line-height: normal; margin: 0px; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none;">T’agrada cantar?</span></li>
<li style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: Times; font-size: 16px; font-stretch: normal; line-height: normal; margin: 0px; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none;">T’agrada jugar a fútbol?</span></li>
<li style="-webkit-text-stroke-color: rgb(0, 0, 0); -webkit-text-stroke-width: initial; font-family: Times; font-size: 16px; font-stretch: normal; line-height: normal; margin: 0px; text-align: justify;"><span style="-webkit-font-kerning: none; font-kerning: none;">T’agrada pescar?</span></li>
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<span style="-webkit-font-kerning: none; font-kerning: none;">1000 persones van contestar afirmativament la primera pregunta , 700 persones la segona ,i 500 la tercera. Quants mentiders hi ha a l’illa?</span></div>
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<tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/18rs9KG8BEMe8SNTMrscFZVglq9x8HfuL/view?usp=sharing"><img border="0" data-original-height="75" data-original-width="100" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieCdEZBhUKpgzHKT7mLzLBKhgJcMjwov2vFS-ILDa3W-Bjn7RCZq8EBvuKaKNOL2GjsLSk-EM6u7ePHmP0Ah7uBkebTmKJkoMN8QBmIdTOmkFZ_-P14-DVATcPLFxHIZXcIvREKHLrR1s/s1600/portanova2bmp.bmp" /></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/18rs9KG8BEMe8SNTMrscFZVglq9x8HfuL/view?usp=sharing">AJUDA I SOLUCIÓ</a></td></tr></tbody></table><div><span style="-webkit-font-kerning: none; font-kerning: none;"><br /></span></div>
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joan parerahttp://www.blogger.com/profile/12035318047168570403noreply@blogger.com0