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#idonthaveasolution

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Christian Lawson-Perfect<p>UPDATE: I misunderstood! The rods have to be in the order 1 ... n, so the solutions in my picture aren't really solutions! This makes the puzzle a lot harder.</p><p>A fun question to start the day from Ali Sada on the math-fun mailing list:</p><p>"What are the triangular numbers, ( T(n) ), such that a chain of rods with lengths 1, 2, ..., ( n ) (connected by hinges) can be arranged to form a rectangle with a perimeter exactly equal to ( T(n) (i.e. using each rod exactly once without any loss or overlap)?"</p><p>If I've understood it correctly, here are two solutions to get started:</p><p><a href="https://mathstodon.xyz/tags/Puzzle" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Puzzle</span></a> <a href="https://mathstodon.xyz/tags/IDontHaveASolution" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>IDontHaveASolution</span></a></p>