March 2005
Shapes
The diagram shows a 4 by 4 grid which contains 3 dots. The grid has been divided into rectangles in such a way that each rectangle has a dot in a corner square (or in an end square if the rectangle is only one square wide).
Can you divide the grid below into 10 rectangles, all of different sizes, so that each one has a dot in a corner square?
(Remember that a square is a type of rectangle, so some of the rectangles could be square.)
Numbers
Four people, A, B, C, and D, each have two coins in their pocket. A has twice as much money as B, who has twice as much as C, who has twice as much as D.
What coins does each person have? (The possible coins are 1p, 2p, 5p, 10p, 20p, 50p, £1, and £2.)
Algebra
The diagram shows a 2 by 2 square. Place numbers in the square so that
- The sum of all four numbers is 340.
- The sum of the two numbers in the first column is twice the sum of the numbers in the first row.
- The sum of the numbers in the second row is three times the sum of the numbers in the second column.
- The sum of the two numbers on each diagonal is the same.
Miscellaneous
The diagram shows a 7 by 7 grid of dots. Some of the dots are marked with numbers.
The puzzle is to draw a continuous line which passes through all 49 dots in the grid. There are 3 rules:
- The line must begin at the dot numbered 1 and pass through each numbered dot in order, ending at the dot numbered 7.
- The line must always be either horizontal or vertical.
- The line can only change direction at a dot.