Copyright © University of Cambridge. All rights reserved.

'Sticky Fingers' printed from

Show menu

Any three positive integers that multiply to make $2009$ would create viable cuboids.
The prime factors of $2009$ are $7\times 7\times 41$, so the options are:
$1 \times1 \times 2009$
$1\times 7\times 287$
$1\times 41\times 49$
$7\times 7 \times 41$

 The first three cuboids all have two faces which each require $2009$ stickers ($1\times2009$, $7\times287$ and $41\times49$ respectively) so Ruth cannot cover them.
The last cuboid has surface area: $2\times( 7\times7+7\times41 + 41\times 7) = 1246$
This leaves $2009-1246=763$ stickers left over.

This problem is taken from the UKMT Mathematical Challenges.
View the archive of all weekly problems grouped by curriculum topic

View the previous week's solution
View the current weekly problem