### 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?

# Tug Harder!

##### Stage: 2 Challenge Level:

You might like to try Tug of War before trying this.

This game is for two players - you can use the interactivity below, or you could draw a number line on a piece of paper and find a counter to use. In both cases, you will need two dice.

Decide who is Positive and who is Negative.
Positive moves from left to right and Negative moves from right to left. (Why do you think we have suggested this way round?)
Take it in turns to throw the two dice and add the scores then move that number of places in your direction.
If the counter reaches -$13$, Negative has won. If the counter reaches $13$, Positive has won.

Is it better to play a game where you have to reach the end exactly, or where you can go over the end? What do you think and why?

Now change the game. This time, when you throw the dice, you can decide whether to add, subtract, multiply or divide the numbers on the dice. You must reach -$13$ or $13$ exactly to win.

Does this make a better game? What do you think? Why or why not?

How else could you change the game?