Creating and manipulating expressions and formulae

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Mind Reading

Age

11 to 14

Challenge level

Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I know?
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One and Three

Age

14 to 16

Challenge level

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400 metres from B. How long is the lake?
$Complex partial fractions$

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Complex Partial Fractions

Age

16 to 18

Challenge level

To break down an algebraic fraction into partial fractions in which all the denominators are linear and all the numerators are constants you sometimes need complex numbers.
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Sums of Pairs

Age

11 to 16

Challenge level

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
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Cubes Within Cubes Revisited

Age

11 to 14

Challenge level

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
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Price Match

Age

7 to 11

Challenge level

Can you find pairs of differently sized windows that cost the same?
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Finding 3D Stacks

Age

7 to 11

Challenge level

Can you find a way of counting the spheres in these arrangements?
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Your Number Is...

Age

7 to 14

Challenge level

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?
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The Number Jumbler

Age

7 to 14

Challenge level

The Number Jumbler can always work out your chosen symbol. Can you work out how?
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Diagonal Sums

Age

7 to 14

Challenge level

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?