### 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?

### Bracelets

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

### Sweets in a Box

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

# Which Is Quicker?

##### Age 7 to 11Challenge Level

Natasha from Moorfield Juniors has answered the first part of this problem. She says:

I thought it would take longer to count in $10$s to $300$ because the numbers were longer.

Idress from Al Ameen school in Dubai agrees with Natasha but adds that for the question of counting in sevens:

We have to add $7$ each time in our head then count so it will take more time than just counting in ones.

Urara and Andra from Canadian Academy in Japan sent in good ideas.

Urara and Andra wrote;

It's much easier to work on this with a partner! When you have timed yourselves and decided about the reasons for your results, you could invent some examples for yourselves. You could predict which was going to be quicker and then try them out to test your prediction ...
$7$ seconds to get to $30$ in ones. $11$ seconds to get to $300$ by tens so counting by ones to get to $30$ is quicker ...
$11$ seconds to get to $40$ in ones. $18$ seconds to get to $4,000$ in hundreds is slower because we normally don't count in hundreds so it takes longer time. But we count by ones often ...
I am slower at counting by sevens because we don't use it very often and we only remember the times table until $7\times12$.

It all helps us to realise that when we are solving problems we have to keep our mind on what is happening as well as just looking at the numbers. A lot of folk did the arithmetic and said that there was no difference. They were looking at the difference in the number of numbers used. But of course the numbers were being said in counting and the people above worked on that idea. Well done!