[math-fun] Five enigmas
In my paper just published in Pour La Science, the French edition of Scientific American, I offer 100 euros + a bottle of champagne on each of these 5 enigmas. Who can construct, or prove the impossibility: 1) 3x3 magic square using 7 or more squared integers different of this only known example (and of its rotations, symmetries and k² multiples): 373² 289² 565² 360721 425² 23² 205² 527² 222121 2) 5x5 bimagic square (using distinct integers) 3) 3x3 semi-magic square of cubes (using distinct positive cubed integers) 4) 4x4 magic square of cubes (using distinct positive cubed integers) 5) ?x?x? multiplicative magic cube using ?^3 distinct integers all smaller than 364. The value of ? is free. Christian. PS on 1): nobody knows a 3x3 magic square of squares. This sub-problem and prize offered since 2005 in the Math Intelligencer should be "easier". PS on 3): "semi-magic" means that we don't take care of the diagonals. PS on 3) and 4): 3x3 magic square of cubes proved impossible.
participants (1)
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Christian Boyer