perplexus.info :: General : Enlargement Maneuver

Enlargement Maneuver (Posted on 2025-01-27)

Four pegs begin on the plane at the corners of a square. At any time, you may cause one peg to jump over a second, placing the first on the opposite side of the second, but at the same distance as before. The jumped peg remains in place. Can you maneuver the pegs to the corners of a larger square?

No Solution Yet Submitted by Danish Ahmed Khan

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integer jumps

Comment 3 of 3 |

I believe Jer's proof is correct. Consider starting with a big square and trying to make a smaller one. It is impossible because all jumps

are displacements of integer multiples of s, where s is the big square side. A jump is (delta_x, delta_y) = (m s, n s) where m and n are integer. s can be non-integer.

Another way to say this is that the original 4 points define a ruled

grid and all moves are constrained to lie on the intersection points of this grid.

Edited on January 28, 2025, 10:53 am

Posted by Steven Lord on 2025-01-27 21:21:19

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