Make Pairs
Problem
Put $10$ counters in a row.
Find a way to arrange the counters into five pairs, one on top of another, evenly spaced in a row so that they look like this:
A counter can only be moved by picking it up, jumping over two counters and landing on another counter.
Can you do it in just five moves?
Getting Started
It might help to make yourself a 'track' with positions numbered for the counters.
How will you remember what you've done so far?
Have you found a good first move? Why is it good?
Student Solutions
This one has had people thinking! Several solutions have been sent in now, but so far only this one, from Hale fits all the 'rules' of the problem.
If the positions are numbered 1 to 10 then:
- 4 to 1
- 6 to 9
- 8 to 3
- 2 to 5
- 10 to 7
Teachers' Resources
Make Pairs
Put $10$ counters in a row.
Find a way to arrange the counters into five pairs, one on top of another, evenly spaced in a row so that they look like this:
A counter can only be moved by picking it up, jumping over two counters and landing on another counter.
Can you do it in just five moves?
Why do this problem?
This problem would be good for children to work on in pairs. It encourages logical thinking and working systematically.Possible approach
Gather children around a table or sit in a circle on the floor. Lay out ten counters as shown and explain the task to the group. Spend some time trying out suggested moves, which will help clarify the 'rules'. Children can then go and work on the task in pairs, using counters or a similar resource.It would be worth having a mini-plenary after 10 minutes or so, to share possible strategies and any insight gained so far.
The final plenary could focus on the solution but equally could involve pairs suggesting advice for other children tackling this task for the first time.