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

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

Solution

| Comment 1 of 3

The task is not possible.

Any sequence of jumps is completely reversible. This means if enlarging a square is possible then reducing would also be possible.

The smallest square on an integer grid has sides of length 1. No jump can bring points to non-integer points, so no smaller square is possible. Hence no bigger square is possible either.

Posted by Jer on 2025-01-27 12:41:48

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info