### Threesomes

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I know?

### Have You Got It?

Can you explain the strategy for winning this game with any target?

# Squares, Squares and More Squares

##### Age 11 to 14 Challenge Level:

Can you dissect a square into:

$4, 7, 10, 13\ldots$ other squares?
$6, 9, 12, 15 \ldots$other squares?
$8, 11, 14 \ldots$other squares?