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'Growing Garlic' printed from http://nrich.maths.org/

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Ben is on the allotment 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 investigate the problem. You can alter the number of bulbs using the up and down arrows, and you can drag them into different arrangements using the little white square.
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