Problems & Puzzles: Puzzles

Problem 72. Consecutive primes inside a 9x9 square such that... A French guy posed the following nice puzzle in his site: "Prove it is possible to fill the 81 cells of a 9x9 grid with the integers from 1 to 81 such as the sum of the numbers inside each 3x3 square is identical" Here are two solution sent in a private emailing circle of friends: 1) By Dwane Campbell: "No rows, columns or diagonals, just the 3x3 sub-squares" having the same sum, 369. 1 32 63 4 35 57 7 29 60 14 45 64 17 39 67 11 42 70 27 46 77 21 49 80 24 52 74 2 33 61 5 36 55 8 30 58 15 43 65 18 37 68 12 40 71 25 47 78 19 50 81 22 53 75 3 31 62 6 34 56 9 28 59 13 44 66 16 38 69 10 41 72 26 48 76 20 51 79 23 54 73 2) By Holger Danielsson: "A pandiagonal magic square of order 9, where each 3x3-subsquare has sum 369", (more than originally asked). 56 18 48 60 14 49 61 10 53 43 73 8 38 81 3 42 77 4 24 68 31 25 64 35 20 72 30 11 54 57 15 50 58 16 46 62 79 1 44 74 9 39 78 5 40 69 32 22 70 28 26 65 36 21 47 63 12 51 59 13 52 55 17 7 37 80 2 45 75 6 41 76 33 23 67 34 19 71 29 27 66 I wonder if a solution exist for some set of 81 consecutive prime integers. Q. Find a solution using 81 consecutive prime integers, for each type, Campbell's and Danielsson's solutions.

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