### 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?

# 9 Weights

##### Stage: 3 Challenge Level:

This problem puts emphasis on trying to gain as much information as possible from each weighing, whatever the outcome. So if a weighing has one outcome which gives you a lot of information, but another outcome which doesn't give you much new information, it is probably not going to be a useful way of identifying the odd weight.

This problem can be extended further by asking how many weights can be sorted in 3 weighings, 4 weighings and more generally n weighings, when you know one is heavier.

To do this, pupils should first try to spot the pattern, then try to explain why this works by looking at what proportion of weights can be discarded at each weighing.

What happens if two of the weights are heavier than the rest? What is the minimum number of weighings now needed to guarantee being able to identify the two heavier weights

A more challenging follow-up problem can be found at The Great Weights Puzzle