Here’s a fun challenge. The task is to fit circles into a grid according to the following rules:

· The centre of every circle must lie on a lattice-point of the grid, and no circles can share the same centre point.

· Every circle must have a whole number as its radius.

· The circles can touch each other and the edge of the grid, but cannot cross. In other words a circle can be entirely inside another, or entirely outside, but not partially inside.

· Your ‘score’ is the total area of all the circles you can fit in. A radius-1 circle has area of 1(pi), a radius-2 circle has an area of 4(pi), radius-3 = 9(pi), etc.

· The example 4 x 4 unit grid has a score of 6(pi) (4+1+1). I have marked the centre of each circle to show that none coincide.

What score can you achieve in the 12 x 12 unit grid?