### Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

# Sticky Fingers

##### Age 14 to 16 ShortChallenge Level

Answer: $763$

Three positive integers that multiply to make $2009$ are:
$1 \times1 \times 2009$
$1\times 7\times 287$
$1\times 41\times 49$
$7\times 7 \times 41$

$1\times1\times2009$ has faces $1\times1$ (two faces), $1\times2009$ (four faces). Not enough stickers for the $2009$ face.

$1\times 7\times 287$ has a face which is $7\times287=2009$ - not enough stickers.
$1\times 41\times 49$ has a face which is $41\times49=2009$ - not enough stickers.

$7\times7\times41$ has faces $7\times7$ (twice) and $7\times41$ (four times)
Surface area $2\times7\times7+4\times41\times 7 = 1246$

This leaves $2009-1246=763$ stickers left over.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.