Broken toaster
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Age
7 to 11
Challenge level
Problem
Image
Only one side of a two-slice toaster is working, so when two slices of bread go in side-by-side, each slice is toasted on one side after 2 minutes, but not on the other.
What is the quickest way to toast both sides of three slices of bread?
What about four slices? Five slices?
Getting Started
Is there a way to make sure both 'slots' of the toaster are always
being used?
Student Solutions
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 $n$ slices of bread it will take $2 \times n$ minutes to toast all the bread.
Teachers' Resources
Why do this problem?
This problem would make a good short challenge, for example
first thing in the morning as you are taking the register. It
requires some logical thinking and quickly leads to a
generalisation.
Key questions
Is there a way to make sure both 'slots' of the toaster are
always being used?
Possible extension
Many children will be able to find a general rule for the
minimum length of time taken for any number of slices of
toast. Can they explain why the rule always
works?
Possible support
Using something to represent the slices of bread might help,
for example, playing cards which are different on each side so that
it is easier to keep track of what has been done.