Creating and manipulating expressions and formulae

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

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?

A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?

Can you prove that twice the sum of two squares always gives the sum of two squares?

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

Account of an investigation which starts from the area of an annulus and leads to the formula for the difference of two squares.

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?