Let $a _ { 1 } , a _ { 2 } , \ldots , a _ { 100 }$ be 100 positive integers. Show that for some $m , n$ with $1 \leq m \leq n \leq 100 , \sum _ { i = m } ^ { n } a _ { i }$ is divisible by 100.
Let $a _ { 1 } , a _ { 2 } , \ldots , a _ { 100 }$ be 100 positive integers. Show that for some $m , n$ with $1 \leq m \leq n \leq 100 , \sum _ { i = m } ^ { n } a _ { i }$ is divisible by 100.