Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Towers

A tower of squares is built inside a right angled isosceles triangle. What fraction of the area of the triangle is covered by the squares?

Framed

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of the pictures.

Guillotine

Age 11 to 14 Short Challenge Level:

$ABCD$ is a rectangle. $P$ is the midpoint of $AD$; the length of $BQ$ is one third the length of $BC$. What fraction of the area of the rectangle is the area of the shaded quadrilateral $ABQP$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

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