2 out of 3
Make some loops out of regular hexagons. What rules can you discover?
2 out of 3
What's the greatest number of sides a polygon on a dotty grid could have?
3 out of 3
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.
3 out of 3
Can you verify and generalise these equations?
3 out of 3
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
3 out of 3
Can you find sets of sloping lines that enclose a square?
3 out of 3
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by 3, 5 and by 7...
3 out of 3
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?
3 out of 3
Delight your friends with this cunning trick! Can you explain how it works?
1 out of 3
