### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

### It Figures

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

### Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

# Which Numbers? (2)

##### Age 7 to 11 Challenge Level:

This problem is similar to Which Numbers? (1), but slightly more tricky. You may like to try that one first.

I am thinking of three sets of numbers less than $101$. They are the blue set, the red set and the black set.
Can you find all the numbers in each set from these clues?

These numbers are some of the blue set: $26, 39, 65, 91$, but there are others too.
These numbers are some of the red set: $12, 18, 30, 42, 66, 78, 84$, but there are others too.
These numbers are some of the black set: $14, 17, 33, 38, 51, 57, 74, 79, 94, 99$, but there are others too.

There are sixteen numbers altogether in the red set, seven numbers in the blue set and fifty numbers in the black set.

These numbers are some that are in just one of the sets: $6,10, 15, 24, 33, 48, 56, 65, 75, 93$, but there are others too.
These numbers are some that are in two of the sets: $12, 13, 36, 54, 72, 96$, but there are others too.
The only number in all three of the sets is $78$.
These numbers are some that are not in any of the sets: $5, 8, 22, 27, 44, 49, 63, 68, 82, 86, 100$, but there are others too.
There are twelve numbers that are in two of the sets.
There are $41$ numbers that are not in any of the sets.

You can download a sheet of all this information that can be cut up into cards.

Can you find the rest of the numbers in the three sets?
Can you give a name to the sets you have found?