### Pyramids

What are the missing numbers in the pyramids?

A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you the last two digits of her answer. Now you can really amaze her by giving the whole answer and the three consecutive numbers used at the start.

# Is it Magic or Is it Maths?

##### Stage: 3 Challenge Level:

Here are three 'tricks' to amaze your friends.

But the really clever trick is explaining to them why these 'tricks' are maths and not magic. Like all good magicians, you should practise by trying them. Can you explain how they work?

 This trick will impress even your maths teacher.
• Think of a number.
• Double it.
• Add $10$.
• Halve it.
• Take away you original number.
• Is your answer $5$?

Try this with a different starting number. Did you get a different result? Why does this happen?
Write the answer on a piece of paper without letting anybody see it and seal it in an envelope. Have somebody hold the envelope and at the end ask them to open it and reveal the number you wrote at the beginning. Wow, Magic!

 Guess how much money people have in their pockets!

Without giving you any information, ask a friend to count the value of some coins and write the amount on a piece of paper. Then ask your friend to:

• Double the amount.
• Add the first odd prime number to the new total.
• Multiply the result by 1/4 of 20.
• Subtract the lowest common multiple of 2 and 3.

For the grand finale, you ask for the final answer. Take off the last digit and you will be able to work out how much the coins are worth!

 Amaze your audience by working out not only their age but also what size shoe they wear! Wow them even more by telling them how the maths works. Give them the following directions but tell them not to show you any calculations: