Creating and manipulating expressions and formulae

problem
More mathematical mysteries

Age

11 to 14

Challenge level

Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try to explain why this works.
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Is it magic or is it maths?

Age

11 to 14

Challenge level

Here are three 'tricks' to amaze your friends. But the really clever trick is explaining to them why these 'tricks' are maths not magic. Like all good magicians, you should practice by trying them. Can you explain how they work?
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Please explain

Age

11 to 14

Challenge level

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain why this works.
problem
Good work if you can get it

Age

11 to 14

Challenge level

A job needs three men but in fact six people do it. When it is finished they are all paid the same. How much was paid in total, and much does each man get if the money is shared as Fred suggests?
problem
Why 8?

Age

11 to 14

Challenge level

Choose any four consecutive even numbers. Multiply the two middle numbers together. Multiply the first and last numbers. Now subtract your second answer from the first. Try it with your own numbers. Why is the answer always 8?
problem
Marbles in a box

Age

11 to 16

Challenge level

How many winning lines can you make in a three-dimensional version of noughts and crosses?
problem
Semi-square

Age

14 to 16

Challenge level

What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?
problem
Square pizza

Age

14 to 16

Challenge level

Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?
problem
A tilted square

Age

14 to 16

Challenge level

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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Back to basics

Age

14 to 16

Challenge level

Find b where 3723(base 10) = 123(base b).