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Omni-MATH / One needs to

Problem

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problem

One needs to ffll the cells of an n×nn\times n table (n>1n > 1) with distinct integers from 11 to n2n^2 so that every two consecutive integers are placed in cells that share a side, while every two integers with the same remainder if divided by nn are placed in distinct rows and distinct columns. For which nn is this possible? (Alexandr Gribalko)
Plain-text mathematical notation (without MathML)
One needs to ffll the cells of an n×n table (n>1) with distinct integers from 1 to n² so that every two consecutive integers are placed in cells that share a side, while every two integers with the same remainder if divided by n are placed in distinct rows and distinct columns. For which n is this possible?

(Alexandr Gribalko)
Original LaTeX notation
One needs to ffll the cells of an $n\times n$ table ($n > 1$) with distinct integers from $1$ to $n^2$ so that every two consecutive integers are placed in cells that share a side, while every two integers with the same remainder if divided by $n$ are placed in distinct rows and distinct columns. For which $n$ is this possible?

(Alexandr Gribalko)

Discussion

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Source and history

task_id
46caf1ee-5b15-5c22-a395-e01323427597
task_key
test--46caf1ee-5b15-5c22-a395-e01323427597
task_revision_id
1
config / split
/ test

Official source

initial import