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Tea Cups

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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Counting on Letters

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

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Teddy Town

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Triangular Clock

Stage: 3 Short Challenge Level: Challenge Level:1

By subtracting 12 from our list of triangle numbers, 3 and 9 must be either side of the 12, and so we will choose to place the 3 on the right. We can keep doing this to get the following:
Clock: going clockwise 12, 3, 7, 8, 2, A, B, C, D, E, F, 9
By the same reasoning A is either 1 or 4, and F is either 1 or 6. But if F=1, then E=4, and so F=6, but 11+6=17 is not a triangle number. So F is not a 1, and so must be a 6.
So E=4, A=1, and so D=11, C=10 and B=5.

This problem is taken from the UKMT Mathematical Challenges.

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