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Omni-MATH / 2500 chess kings have to be placed on a 100×100 chessboard so that

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problem

2500 chess kings have to be placed on a 100×100100 \times 100 chessboard so that [b](i)[/b] no king can capture any other one (i.e. no two kings are placed in two squares sharing a common vertex); [b](ii)[/b] each row and each column contains exactly 25 kings. Find the number of such arrangements. (Two arrangements differing by rotation or symmetry are supposed to be different.) [i]
Plain-text mathematical notation (without MathML)
2500 chess kings have to be placed on a 100×100 chessboard so that

[b](i)[/b] no king can capture any other one (i.e. no two kings are placed in two squares sharing a common vertex);
[b](ii)[/b] each row and each column contains exactly 25 kings.

Find the number of such arrangements. (Two arrangements differing by rotation or symmetry are supposed to be different.)

[i]
Original LaTeX notation
2500 chess kings have to be placed on a $100 \times 100$ chessboard so that

[b](i)[/b] no king can capture any other one (i.e. no two kings are placed in two squares sharing a common vertex);
[b](ii)[/b] each row and each column contains exactly 25 kings.

Find the number of such arrangements. (Two arrangements differing by rotation or symmetry are supposed to be different.)

[i]

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Source and history

task_id
f346f4b3-500f-5758-9746-4a191e5fa2ff
task_key
test--f346f4b3-500f-5758-9746-4a191e5fa2ff
task_revision_id
1
config / split
/ test

Official source

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