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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?

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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?

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Tilted Squares

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Framed

Age 11 to 14 Challenge Level:

Seven small pictures, all square or rectangular, with sides measuring a whole number of inches and each with a different area, have frames exactly one inch wide.

In each case the area of the frame is either the same as the area of the picture or a multiple of it.

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, show how they fit together to make a rectangle, and find the width of the rectangle.