Brainteasers

28th November 2003 at 00:00
Age 7-11

Magic square

This is a magic square. The numbers in any row, column or diagonal have the same total.

But one of the numbers is incorrect.

Which number is it?

What should it be?

Age 11-14

Differences

Find the two smallest whole numbers where the difference of their squares is a cube, and the difference of their cubes is a square.

Brainteaser solutions from page 30

Magic square

23 10 17 4 11

6 18 5 12 24

19 1 13 25 7

2 14 21 8 20

15 22 9 16 3

Differences

The smallest whole numbers are 6 and 10:

102 - 62 = 100 - 36 = 64 = 43

103 - 63 = 1,000 - 216 = 784 = 282

Magic square

23 10 17 4 11

6 18 5 12 24

19 1 13 25 7

2 14 21 8 20

15 22 9 16 3

Differences

The smallest whole numbers are 6 and 10:

102 - 62 = 100 - 36 = 64 = 43

103 - 63 = 1,000 - 216 = 784 = 282

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