Kate has made a birthday cake for her Granny’s birthday. The cake has candles to show Granny’s age in years.

Tall candles represent 10 years and short candles represent 1 year. There are 12 candles altogether.

Kate thinks this is lucky, since her Granny’s age in years is 12 times Kate’s lucky prime number.

What is Kate’s lucky prime number?

Old folk’s home

A home for elderly people has 26 rooms. There are single rooms for widows or widowers on their own, and double rooms for married couples.

15 men and 23 women live at the home.

How many married couples are there?

SOLUTIONS Granny’s birthday (ages 8 to 12) Kate’s lucky prime number is 7.

The candles could represent an age of 39, 48, 57, 66, 75, 84 or 93. Only 48 and 84 are multiples of 12, and 4 is not a prime number.

Old folk’s home (ages 9 to 14) 12 couples, 3 widowers and 11 widows. If A is the number of widows, B the number of married men (or women), and C the number of widowers, then A + B= 23, B + C = 15, giving A + 2B + C = 38. But A +B+C= 26, so B = 12.