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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...

Mind Reading

Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I know?

How Many Miles to Go?

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

Number Pyramids

Age 11 to 14 Challenge Level:

In a number pyramid, the numbers on the lower layers determine the numbers above them.

Start by choosing three single-digit numbers and enter them in the bottom row of the interactive number pyramid.

Try entering some different numbers in the bottom row - you don't have to stick to single-digit numbers.
Can you work out how the numbers in the upper layers are generated?
Here are some questions to consider:

If I tell you the numbers on the bottom layer, can you work out the top number without working out the middle layer?

If you change the order of the numbers on the bottom layer, will the top number change? 

Given any three numbers for the bottom, how can you work out the largest possible number that could go at the top?

If I give you a target for the top number, can you quickly find three possible numbers for the bottom?

Can you adapt what you discovered about 3-layer pyramids to larger pyramids?

Here is an interactive number pyramid with four layers so you can test out your ideas.

You might now like to have a go at More Number Pyramids