Sunday Times Teaser 2650 – Squares of Oblongs
by Des MacHale
I gave a set of nine rectangular cards of dimensions 1×2, 2×3, 3×4, 4×5, 5×6, 6×7, 7×8, 8×9 and 9×10 to each of two friends.
I asked each of them to arrange some of their cards to form a complete square and it turned out that those they made were the smallest and the largest that were possible.
What, in increasing order, were the sizes of all the unused cards?