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Brainteasers

pt = Pigeons and hedgehogs

Zak has a large garden.

On Tuesday, he saw pigeons and hedgehogs in his garden. He counted 24 heads and 56 feet altogether.

1. How many pigeons and how many hedgehogs could he see?

2. What if he could see 36 heads and 100 feet?

Magic cubes

The number 370 is the sum of the cubes of its three digits:

There are just three other three-digit numbers that have this property.

What are they?

SOLUTIONS Pigeons and hedgehogs (ages 7 to 12) 1. 20 pigeons and 4 hedgehogs. 2. 22 pigeons and 14 hedgehogs. Systematic working through the possibilities will find the answer.

Cubes (ages 14 to 16) 153, 371 and 407. You could use a spreadsheet to solve this problem by working systematically through the three-digit numbers from 100.

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