with the two versions, records should be the same for 4x4 and above.
... Yes, you're right ! Best, É. -----Message d'origine----- De : math-fun-bounces+eric.angelini=kntv.be@mailman.xmission.com [mailto:math-fun-bounces+eric.angelini=kntv.be@mailman.xmission.com] De la part de Christian Boyer Envoyé : jeudi 18 avril 2013 13:55 À : 'math-fun' Objet : Re: [math-fun] A grid with MAX Sure Eric, your version is much more logical, I like it! And with the two versions, records should be the same for 4x4 and above. Christian. -----Message d'origine----- De : math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] De la part de Eric Angelini Envoyé : jeudi 18 avril 2013 12:58 À : math-fun Objet : Re: [math-fun] A grid with MAX
the rules are different!
Yes, I know, Christian, Oui, je sais, Christian, But the rules in Le Monde's video Mais les règles dans la vidéo du Monde Are not consistent: Ne sont pas cohérentes : Why does he put a second "1" in an isolated cell with no neighbors? Pourquoi inscrit-il un second "1" dans une cellule sans voisins ? I think that the corrected version is simpler and more logical: Occam's razor! Comprends-je toujours le français ? Ma version est meilleure, non ? Regards, Regards. ;-D É. -----Message d'origine----- De : math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] De la part de Christian Boyer Envoyé : jeudi 18 avril 2013 11:58 À : 'math-fun' Objet : Re: [math-fun] A grid with MAX Hmmm... if we carefully listen (in French) the original 3x3 problem in "Le Monde" website, http://bit.ly/12RaSEi, the rules are different! Eric, maybe you no more speak French? ;-) The BEGINNING of the game is different: we first have to choose two cells (not necessarily neighboring), placing 1 in these two cells. Then the rules are the same: each new chosen cell is filled with the sum of the neighboring cells. With these rules, the new max for 3x3 is no more 44, but 57 (I think): 1 2 1 3 7 30 10 20 57 However, this should not change the records of bigger grids. On 4x4, 5x5,... it's more interesting to place the two first 1 in the same corner, meaning that the rules become equivalent. Christian. -----Message d'origine----- De : math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] De la part de Eric Angelini Envoyé : dimanche 14 avril 2013 16:12 À : math-fun Cc : alexandre.wajnberg@skynet.be Objet : [math-fun] A grid with MAX Hello MathFunsters, I've seen this on "Le Monde" webpage. http://bit.ly/12RaSEi Draw a 3x3 square and write "1" in the upper left corner-square. Fill now one by one the other squares according to these rules: - select an empty square - write in it the sum of its neighboring squares (a "corner-square" has 3 neighbours, an "edge-square" 5 and the "center-square" 8) - when all squares are marked, record the highest written value. Example: +-----+-----+-----+ | 1 | | | | | | | +-----+-----+-----+ | | | | | | | | +-----+-----+-----+ | | | | | | | | +-----+-----+-----+ +-----+-----+-----+ | 1 | | | | | | | +-----+-----+-----+ | | | | | | | | +-----+-----+-----+ | | | 0 | | | | | +-----+-----+-----+ +-----+-----+-----+ | 1 | 1 | | | | | | +-----+-----+-----+ | | | | | | | | +-----+-----+-----+ | | | 0 | | | | | +-----+-----+-----+ +-----+-----+-----+ | 1 | 1 | | | | | | +-----+-----+-----+ | | 2 | | | | | | +-----+-----+-----+ | | | 0 | | | | | +-----+-----+-----+ +-----+-----+-----+ | 1 | 1 | 3 | | | | | +-----+-----+-----+ | | 2 | | | | | | +-----+-----+-----+ | | | 0 | | | | | +-----+-----+-----+ +-----+-----+-----+ | 1 | 1 | 3 | | | | | +-----+-----+-----+ | | 2 | 6 | | | | | +-----+-----+-----+ | | | 0 | | | | | +-----+-----+-----+ +-----+-----+-----+ | 1 | 1 | 3 | | | | | +-----+-----+-----+ | | 2 | 6 | | | | | +-----+-----+-----+ | | 8 | 0 | | | | | +-----+-----+-----+ +-----+-----+-----+ | 1 | 1 | 3 | | | | | +-----+-----+-----+ | | 2 | 6 | | | | | +-----+-----+-----+ | 10 | 8 | 0 | | | | | +-----+-----+-----+ +-----+-----+-----+ | 1 | 1 | 3 | | | | | +-----+-----+-----+ | 22 | 2 | 6 | <--- MAX value = 22 | | | | +-----+-----+-----+ | 10 | 8 | 0 | | | | | +-----+-----+-----+ My best MAX is 40: is it the highest possible MAX in a 3x3 square? What are, if we consider all nxn squares, the MAX values for the first n? The sequence of such MAX starts with S(max) = 1,4,... then what? This is perhaps old hat, sorry -- but there are too many seqs in the OEIS that start with 1,4,... Best, E. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun