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square by n sticks of lengths 1,2, 3,..., n 2018 Malaysia OMK Intermediate B1

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September 19, 2021
combinatorics

Problem Statement

Let nn be an integer. Dayang are given nn sticks of lengths 1,2,3,...,n1,2, 3,..., n. She may connect the sticks at their ends to form longer sticks, but cannot cut them. She wants to use all these sticks to form a square. For example, for n=8n = 8, she can make a square of side length 99 using these connected sticks: 1+81 + 8, 2+72 + 7, 3+63 + 6, and 4+54 + 5. How many values of nn, with 1≤n≤20181 \le n \le 2018, that allow her to do this?
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