### 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:

In a similar way to Which Numbers? (1) the solutions we had tended to identify correctly two of the sets but struggled with the third.

Joshua of Crookhill Primary School said:

For the red group it is all the multiples of $6$.
For the blue group it is $+ 13$ every time.
and for the black we have no idea what so ever!

Sophie and Jo of Huish Primary continued:

The blue set's give away numbers are $26, 39, 65$ and $91$. We first looked at the end digits and saw they were going up by $3$ each time. We then knew it was a multiple of somthing with a $3$ on the end. We then knew they were going up by $10$ each time. We added the $10$ and the $3$ together to get $13$.  So the blue set is going up by $13$ each time: $\{13,26,39,52,65,78,91\}$. There are $7$ numbers in the blue which is the same as on the sheet.

The red set's give away numbers are $12, 18, 30, 42, 66, 78, 84$. We knew they were even, so it would be in either the $2$s, $4$s, $6$s or $8$s. We narrowed it down to the $6$s and the $2$s. The $2$s has $50$ numbers less than $101$, so we knew it was the $6$s. There were $16$ numbers in the red set like it said on the sheet: $\{6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96\}$.

The black set's give away numbers are $14, 17, 33, 38, 51, 57, 74, 79, 94, 99$. We thought a long time about what it could be. As we looked closer we realised that the $10$s digit was always odd. We also realised that there are $50$ numbers with an odd $10$s digit before $101$. So the black set is all the $10$s, $30$s, $50$s, $70$s and $90$s.

Do you agree with Sophie and Jo?