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# 9 Weights

### First Puzzle:

### Second Puzzle:

### Third Puzzle:

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Age 11 to 14

Challenge Level

You have been given 9 weights, one of which is slightly heavier than the rest, and a balance so that you can compare them.

Can you **always** work out which weight is heavier in just **two weighings** of the balance?

Could you **always** work out which is heavier in just two weighings if you had been given 10 weights?

You have now been given 27 weights, one of which is slightly heavier than the rest.

Can you **always** work out which weight is heavier in just **three weighings** of the balance?

You now have 9 weights again, and know that one is a slightly different weight, but you don't know if it is heavier or lighter.

Can you explain how you would **always** be able to tell which weight is different, and whether it is heavier or ligther, in just **three weighings** ?

Could you **always** work out which is the odd one out in just three weighings if you had been given 10 weights?

A very challenging follow-up puzzle that you might like to try is The Great Weights Puzzle.

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

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.

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?