The Vegetable Garden

Ben is in the vegetable garden with his Mum. They would like to grow some garlic and are deciding how to plant the garlic cloves.

Ben arranges the cloves into three rows and finds that he has one spare clove. How many cloves might he have had to start with?

Ben plants cloves of garlic in two rows and has one clove left over. So he tries again.
He plants cloves in three rows and has one left over. So he tries again.
He plants cloves in four rows and has one left over. So he tries again.
He plants cloves in five rows and has one left over. So he tries again.
He plants cloves in six rows and has one left over.
We know that he has fewer than 100 garlic cloves. How many did he have?
You could think about how many cloves he might have had if there were more than 100.

You might like to use this interactivity to try out your ideas: