### Counting Counters

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

### Cuisenaire Rods

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

### Doplication

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

# Broken Toaster

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

Erika sent us her very thoughtful solution. Well done!

If there are three slices of bread, there are a total of 6 "sides" to be toasted As we can only toast 2 sides at a time, and toasting two sides takes 2 minutes, it will take at least 6 minutes to toast all the bread. Also, each slice must go in the toaster twice, and we can toast two different slices at once. We can toast all three slices by doing
• 1 and 2
• 3 and 2
• 1 and 3
If there are 4 slices of bread, there are a total of 8 "sides", so it will take 8 minutes to toast all the bread. We can do slices 1 and 2 in the first 4 minutes (turning them over after 2 minutes), and 3 and 4 in the last 4 minutes (turning them over after two minutes). If there are 5 slices it will take 10 minutes.

If there are $n$ slices of bread it will take $2 \times n$ minutes to toast all the bread.