### Ultra bimagic 25x25 square

Â

Harm Derksen introduced onÂ his website http://www.math.lsa.umich.edu/~hderksen/magic.html an ultra bimagic 25x25 square.Â The 25x25 magicÂ square is panmagicÂ and eachÂ 1/5 row/column/diagonalÂ gives 1/5Â of theÂ magic sum.Â Fill inÂ number xÂ numberÂ instead of eachÂ numberÂ and each row/column/diagonalÂ gives the bimagic sumÂ of 3263025.

UseÂ 2xÂ the sameÂ or 2 differentÂ panmagic 5x5Â squaresÂ to construct theÂ ultra bimagic 25x25Â square.Â Each grid consists ofÂ 25xÂ the (on the 2x2 carpet)Â shifted versionsÂ of the panmagic 5x5 square.

2x2Â carpetÂ of firstÂ panmagic 5x5 sq.Â Â Â Â 2x2Â carpet of secondÂ panmagic 5x5 sq.

 25 1 7 13 19 25 1 7 13 19 Â Â 1 15 22 18 9 1 15 22 18 9 12 18 24 5 6 12 18 24 5 6 Â Â 23 19 6 5 12 23 19 6 5 12 4 10 11 17 23 4 10 11 17 23 Â Â 10 2 13 24 16 10 2 13 24 16 16 22 3 9 15 16 22 3 9 15 Â Â 14 21 20 7 3 14 21 20 7 3 8 14 20 21 2 8 14 20 21 2 Â Â 17 8 4 11 25 17 8 4 11 25 25 1 7 13 19 25 1 7 13 19 Â Â 1 15 22 18 9 1 15 22 18 9 12 18 24 5 6 12 18 24 5 6 Â Â 23 19 6 5 12 23 19 6 5 12 4 10 11 17 23 4 10 11 17 23 Â Â 10 2 13 24 16 10 2 13 24 16 16 22 3 9 15 16 22 3 9 15 Â Â 14 21 20 7 3 14 21 20 7 3 8 14 20 21 2 8 14 20 21 2 Â Â 17 8 4 11 25 17 8 4 11 25

Â

Â Take 1x number from first grid with 25xÂ shifted version of the firstÂ panmagic 5x5 square

 8 14 20 21 2 15 16 22 3 9 17 23 4 10 11 24 5 6 12 18 1 7 13 19 25 25 1 7 13 19 2 8 14 20 21 9 15 16 22 3 11 17 23 4 10 18 24 5 6 12 12 18 24 5 6 19 25 1 7 13 21 2 8 14 20 3 9 15 16 22 10 11 17 23 4 4 10 11 17 23 6 12 18 24 5 13 19 25 1 7 20 21 2 8 14 22 3 9 15 16 16 22 3 9 15 23 4 10 11 17 5 6 12 18 24 7 13 19 25 1 14 20 21 2 8 22 3 9 15 16 4 10 11 17 23 6 12 18 24 5 13 19 25 1 7 20 21 2 8 14 14 20 21 2 8 16 22 3 9 15 23 4 10 11 17 5 6 12 18 24 7 13 19 25 1 1 7 13 19 25 8 14 20 21 2 15 16 22 3 9 17 23 4 10 11 24 5 6 12 18 18 24 5 6 12 25 1 7 13 19 2 8 14 20 21 9 15 16 22 3 11 17 23 4 10 10 11 17 23 4 12 18 24 5 6 19 25 1 7 13 21 2 8 14 20 3 9 15 16 22 11 17 23 4 10 18 24 5 6 12 25 1 7 13 19 2 8 14 20 21 9 15 16 22 3 3 9 15 16 22 10 11 17 23 4 12 18 24 5 6 19 25 1 7 13 21 2 8 14 20 20 21 2 8 14 22 3 9 15 16 4 10 11 17 23 6 12 18 24 5 13 19 25 1 7 7 13 19 25 1 14 20 21 2 8 16 22 3 9 15 23 4 10 11 17 5 6 12 18 24 24 5 6 12 18 1 7 13 19 25 8 14 20 21 2 15 16 22 3 9 17 23 4 10 11 5 6 12 18 24 7 13 19 25 1 14 20 21 2 8 16 22 3 9 15 23 4 10 11 17 17 23 4 10 11 24 5 6 12 18 1 7 13 19 25 8 14 20 21 2 15 16 22 3 9 9 15 16 22 3 11 17 23 4 10 18 24 5 6 12 25 1 7 13 19 2 8 14 20 21 21 2 8 14 20 3 9 15 16 22 10 11 17 23 4 12 18 24 5 6 19 25 1 7 13 13 19 25 1 7 20 21 2 8 14 22 3 9 15 16 4 10 11 17 23 6 12 18 24 5 19 25 1 7 13 21 2 8 14 20 3 9 15 16 22 10 11 17 23 4 12 18 24 5 6 6 12 18 24 5 13 19 25 1 7 20 21 2 8 14 22 3 9 15 16 4 10 11 17 23 23 4 10 11 17 5 6 12 18 24 7 13 19 25 1 14 20 21 2 8 16 22 3 9 15 15 16 22 3 9 17 23 4 10 11 24 5 6 12 18 1 7 13 19 25 8 14 20 21 2 2 8 14 20 21 9 15 16 22 3 11 17 23 4 10 18 24 5 6 12 25 1 7 13 19

Â

Â

+ 25 x [number -/- 1] from second grid with 25xÂ shifted version of the secondÂ panmagic 5x5 sq.

 17 8 4 11 25 21 20 7 3 14 13 24 16 10 2 5 12 23 19 6 9 1 15 22 18 1 15 22 18 9 8 4 11 25 17 20 7 3 14 21 24 16 10 2 13 12 23 19 6 5 23 19 6 5 12 15 22 18 9 1 4 11 25 17 8 7 3 14 21 20 16 10 2 13 24 10 2 13 24 16 19 6 5 12 23 22 18 9 1 15 11 25 17 8 4 3 14 21 20 7 14 21 20 7 3 2 13 24 16 10 6 5 12 23 19 18 9 1 15 22 25 17 8 4 11 15 22 18 9 1 4 11 25 17 8 7 3 14 21 20 16 10 2 13 24 23 19 6 5 12 19 6 5 12 23 22 18 9 1 15 11 25 17 8 4 3 14 21 20 7 10 2 13 24 16 2 13 24 16 10 6 5 12 23 19 18 9 1 15 22 25 17 8 4 11 14 21 20 7 3 21