Or rather, "since this s'>m/3", as it always is. If s'<=m/3, t>=2m/3, i.e. the longest length is at least twice the shortest length and there can't be a simple counting argument that means you can't fill up an n-stick. You just fill it up with copies of t until you get stuck; then you remove your last copy of t and fill up the remaining gap with two equal sized sticks, which are obviously shorter than t and longer than s.
no subject
Or rather, "since this s'>m/3", as it always is. If s'<=m/3, t>=2m/3, i.e. the longest length is at least twice the shortest length and there can't be a simple counting argument that means you can't fill up an n-stick. You just fill it up with copies of t until you get stuck; then you remove your last copy of t and fill up the remaining gap with two equal sized sticks, which are obviously shorter than t and longer than s.