Here is a 2-by-2 grid.
The numbers are the totals of the rows and columns.
Write a number in each box on the grid.
The rows and columns must add up to the totals shown.
Find five different ways to do it.
TIN OF PAINT
A tin of paint weighs 5kg when it is half full of paint.
It weighs 4kg when it is one third full of paint.
What is the weight of a full tin of paint?
Tin of paint: Imagine weighing scales with a half-full tin of paint on one side and a tin of paint one-third full on the other. The side that's heavier is so by 1kg. The difference is the extra weight of the paint on that side, since there is a tin on each side. The difference between one half of the paint and one third of the paint is one sixth, which is 1kg. So the weight of the paint in a full tin is 6kg. Since a half-full tin weighs 5kg, and half the paint weighs 3kg, the tin must weigh 2kg. Therefore, a full tin weighs 8kg.