What am I?

1) I am thinking of a five-digit number.

The digit 6 is three places before the digit 4.

The digit 1 is three places before the digit 2.

The digit 2 is after the digit 8 but before the digit 4.

What number am I thinking of?

2) I am thinking of a pair of numbers.

The sum of the two numbers is 20.

The product of the two numbers has a units digit of 1.

The difference between the two numbers is less than 10.What two numbers am I thinking of?

SOLUTION What am I? (ages 7 to 10) 1) 16824; 2) 7 and 13. The two numbers must end in 7 and 3 or 9 and 9. As their sum is 20, two possibilities are 17 and 3, or 13 and 7. As their difference is less than 10, the pair of numbers must be 7 and 13.

Odd one out

Nasreen has eight balls which are exactly the same size and colour.

One of the balls is heavier than all the rest but the difference is so slight she cannot tell by simply holding them in her hands.

Using a pair of balance scales only twice, how can Nasreen tell which is the odd ball?

SOLUTION Odd one out (ages 9 to 14) Weigh three balls against any other three balls. If they balance, weigh the remaining two balls against each other and the heavier one will go down. If the original six balls don’t balance, take two of the balls from the heavier tray and weigh them against each other. If one goes down it is the heavier ball; if they balance, the third ball is the odd one out.