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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?

Always the Same

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

Fibs

The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?

Your Number Is...

Age 7 to 14 Challenge Level:

Press the button in the interactivity below, and see what happens:

Now try again starting with a different number.

Try again.

Try starting with a fraction... or decimal... or negative number...

Why are your answers ALWAYS the same?


Can you design instructions for similar "Think of a number" machines of your own?
Test them on a partner to check that they lead to your anticipated solutions.
 
 
You may want to take a look at Your Number Was... for a suitable follow-up activity.