In the diagram below, there are 15 counters. Andrew thinks they look like a fish swimming to the left.
He wonders if he can make it swim to the right. Yes, he can. But what is the smallest number of counters that he needs to move to make the fish swim to the right?
Solution
Andrew manages to make the fish swim in the opposite direction by moving just five coins.
He took the five different coins marked by an outline and moved them to the circles marked with a dotted outline. Now he has the fish swimming to the right! Are there any other ways to do this?
Can he be sure that he can’t do this by moving less than 5 coins?
Extension
How many coins do you need to move if there are just 6 coins to start with; just 10; or even 21? Do you see any patterns here?