Give a proof by contradiction to show that if the odd integers $1,3,5,7,9,11,13,15,17,19,$ are placed randomly around a circle (without repetition), then there must exist three adjacent numbers along the circle whose sum is greater than $32$
How do you approach these problems, I feel lost on how to solve it.
Thank you
Best Answer
The numbers other than 1 sum to $99$. Splitting the $9$ of them into three consecutive triples, one must sum to at least $33$.