May 2005
Shapes
The diagram shows a 5 by 5 grid with several coloured squares of different sizes. The coloured squares do not touch each other, not even corner-to-corner. The numbers to the left and above the grid show the numbers of grid squares that are occupied by the coloured squares in each row and column.
Can you shade the 10 by 10 grid below in the same way?
Try to avoid using trial and error. The puzzle can be solved logically.
Numbers
The diagram shows a multiplication sum. Each ‘D’ stands for an odd digit, and each ‘E’ stands for an even digit. The ‘0’ is a zero, put there because on that line we are multiplying by the tens digit.
Can you work out what the sum is?
Explain the logic that you use.
Algebra
Mr and Mrs Series have had 5 children at regular intervals, so that their ages are all equally spaced. The sum of the ages of the two eldest children is equal to the sum of the ages of the three youngest children.
What is the ratio of the ages of the eldest child and the youngest child?
Miscellaneous
Gina was admiring Mr Smith’s collection of budgerigars, which he kept in large cages in his back garden. ‘There are so many!’ she said.
‘Between two and three hundred’, said Mr Smith. ‘I keep the same number in each cage, so as not to overcrowd them.’
‘How many do you have in each cage?’ Gina asked.
‘If I tell you my exact number of birds, you can work it out’, he replied.
‘But I don’t know how many cages you have either’, said Gina.
‘You can still do it’, said Mr Smith.
And she did. Can you? How many birds are there in each cage? And how many cages?