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 Question from Emma, a parent: Grandpa had an apple tree. On the first day half of the apples plus one fell to the ground. On the second day, half of the remaining apples plus one fell to the ground. On the third day, half of what was left plus one fell to the ground. The tree was left with only one apple now. How many apples did the tree produce originally?

Hi Emma,

This type of problem I call "working backwards". The technique is to start at the end of day three when there is one apple left and work backwards to find out how many apples were left at the end of day two.

Ask your child, if on day three half the apples plus one fell of the tree and only one remained how many apples were there at the beginning of day three? The answer can't be two as as half the apples plus one is two leaving no apples on the tree. The answer can't be three as half of three is one and a half and one and a half apples plus one can't fall from the tree. If there were four apples at the beginning of day three then half of four plus one is two plus one which is three. This would leave one apple on the tree and hence at the beginning of day three, which is the same as the end of day two, there are 4 apples on the tree.

Now ask your child, if on day two half the apples plus one fell of the tree and only four remained how many apples were there at the beginning of day two? How many apples were there at the beginning of day 1?