### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

### Summing Consecutive Numbers

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

### 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?

# Your Number Is...

##### Stage: 3 Challenge Level:

Press the start button and see what happens:

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Now try again starting with a different number.

Try again.

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

Why is the answer ALWAYS the same?

Can you design instructions for similar machines of your own?

You may want to take a look at  Your Number Was... for a suitable follow-up activity.