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6 holes in 3x1 paper, folded twice to give a square side 1

Source: 1970 Swedish Mathematical Competition p5

March 21, 2021
geometrysquare

Problem Statement

A 3×13\times 1 paper rectangle is folded twice to give a square side 11. The square is folded along a diagonal to give a right-angled triangle. A needle is driven through an interior point of the triangle, making 66 holes in the paper. The paper is then unfolded. Where should the point be in order to maximise the smallest distance between any two holes?
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