### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### 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.

### 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?

# Triangular Clock

##### Stage: 3 Short Challenge Level:

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:

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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