perplexus.info :: Just Math : Pick Up More Sticks

Pick Up More Sticks (Posted on 2025-05-27)

You have N sticks with lengths 1, 2, 3, ..., N.
Provide a closed form function in terms of N for the number of distinct valid triangles can you make from these N sticks.

note: reflections and rotations are considered to be the same, and valid triangles must have positive area.

Inspired by 5, 6, Pick Up Sticks

Submitted by Larry

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Solution: (Hide)

f(n) = ( 4*n^3 - 18*n^2 + 20*n - 3 + 3*(-1)^n )/48
which, rearranged, is identical to the formula in Charlie's second post.
results from 0 to 30:
[0, 0, 0, 0, 1, 3, 7, 13, 22, 34, 50,
70, 95, 125, 161, 203, 252, 308, 372, 444, 525,
615, 715, 825, 946, 1078, 1222, 1378, 1547, 1729]

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: computer solution	Charlie	2025-05-27 10:29:01
computer solution	Charlie	2025-05-27 09:37:45

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