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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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Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

9 Weights

Stage: 3 Challenge Level: Challenge Level:1

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