# Brainteasers

Two triangles

Take two congruent obtuse-angled scalene triangles.

How many different shapes can you make by fitting both triangles together edge to edge?

Reversing the digits

Find a four-digit number such that the number formed by reversing the digits is four times the original number.

ABCD x 4 = DCBA

SOLUTIONS Two triangles (ages 7 to 10) You can make three different parallelograms, a kite and two different inverted kites or deltas.

Reversing the digits (ages 10 to 14) The number is 2178. A must be even because D x 4 gives a number whose units digit is A. A must be 2 because A x 4 plus any carry figure from the hundreds gives a number less than 10. So D could be 8 or 9. D must be 8 because 8 x 4 ends in 2 and 9 x 4 does not.

B x 4 gives a number less than 10 since there is no carry figure to the thousands. B must be different from A, so B is 1. We now have 21C8 x 4 = 8C12. C must be 7 since it is the only digit which, when multiplied by 4 and 3 added, gives a number ending in 1.

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