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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?

Forgotten Number

I have forgotten the number of the combination of the lock on my briefcase. I did have a method for remembering it...

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Sam displays cans in 3 triangular stacks. With the same number he could make one large triangular stack or stack them all in a square based pyramid. How many cans are there how were they arranged?

Handshakes

Age 11 to 14
Challenge Level

If you were one of ten people at a party, how many times would you shake hands?
How many times would everyone else shake hands?
How could you use this to work out the total number of handshakes?
Check your method makes sense by trying some examples of small gatherings.