### Month Mania

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

### Neighbours

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

### Page Numbers

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

# Which Is Quicker?

##### Stage: 2 Challenge 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!