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Summing Consecutive Numbers

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Shopping Basket

The items in the shopping basket add and multiply to give the same amount. What could their prices be?


Can you work out how to win this game of Nim? Does it matter if you go first or second?


Age 11 to 14
Challenge Level

Take a look at this video.


Can you work out how Charlie ordered the cards to perform the trick?

Once you've had a chance to think about it, click below to see some suggested starting points:

Charlie started by thinking:

“Ace” has three letters so it should go in third place. “Two” has three letters so it should go in sixth position. “Three” has five letters so it should go in eleventh position. “Four” has four letters so it should go in fifteenth position...

Luke started by thinking:

I should be able to work backwards, so I'll start with just the Jack, Queen and King and see what happens...

Alison started by thinking:

If I arrange the cards from Ace to King to do the trick, I won't reveal the cards in the right order. But I could keep a record of the sequence they come out in...

Can you take each of their starting ideas and develop them into a solution?

Can you use each method to perform the trick in a different language, or with two suits of cards together, or in reverse order from King to Ace, or...?

You may be interested in the other problems in our Seeing mathematically Feature.