Could you please help me find the answer to this question. I think it has something to do with grouping or pairing some numbers.I would appreciate easy-to-understand solutions. Thank you.
There are 99 sticks of lengths 1,2,3...,99 respectively, the width of the sticks can be ignored. Is it possible to form the perimeter of a rectangle using all the sticks?
Hint: Use $1,2,$ and $3$ for the short ends of the rectangle. That leaves $4,5,\ldots,99$ to divide into two equal sets. Note that $4+99=5+98=\cdots=51+52$. How many such pairs are there?