Mental calculations

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?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Find at least one way to put in some operation signs to make these digits come to 100.

What do you notice about these squares of numbers? What is the same? What is different?

Can you work out what a ziffle is on the planet Zargon?

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Can you find two butterflies to go on each flower so that the numbers on each pair of butterflies adds to the number on their flower?