Puzzle 1277 Square grids and
coprimes touching pairs
On July 19, 2026, Gioregos Kalogeropoulos wrote:
Reed Silverstein who is a member of "Recreational
Maths & Math Puzzles" discord server gave me the
permission to send you this original puzzle that he
made:
The puzzle: arrange the numbers 1 through
n^2 in an n×n grid
to minimize how many
touching pairs are coprime. Touching means
sharing an edge (up/down/left/right) aka von
neumann neighborhood. Here are optimal grids for
2×2 through 7×7, with minimums 3, 6, 6, 10, 11,
16...
Reading the picture: green line =
coprime pair, dashed red = shared factor, shaded
cells = evens.
Q1. Can you verify these results?
Q2. Can you extend the sequence?
Q3.
Send your best result for a grid 100x100
