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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?

Human Food

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?

Sam Again

Here is a collection of puzzles about Sam's shop sent in by club members. Perhaps you can make up more puzzles, find formulas or find general methods.

Forgotten Number

Age 11 to 14 Challenge Level:

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

It went as follows:

    The number is equal to the sum of the cubes of its own digits.

      It is a three digit number less than 500

        It is the sum of consecutive factorials.

          It is a triangle number.