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2021 JMPSC Invitationals Problems/Problem 5

Revision as of 15:02, 11 July 2021 by Samrocksnature (talk | contribs) (Created page with "==Problem== An <math>n</math>-pointed fork is a figure that consists of two parts: a handle that weighs <math>12</math> ounces and <math>n</math> "skewers" that each weigh a n...")
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Problem

An $n$-pointed fork is a figure that consists of two parts: a handle that weighs $12$ ounces and $n$ "skewers" that each weigh a nonzero integer weight (in ounces). Suppose $n$ is a positive integer such that there exists a fork with weight $n^2.$ What is the sum of all possible values of $n$?

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Solution

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