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During a recent expedition, three intrepid adventurers were left stranded in the middle of the desert with only a crate full of apples.

During the night, Alan woke up and decided to hide his share of the apples and hid a third, then promptly fell asleep again.

Brian woke up shortly after and also decided to hide a third of the remaining apples and he also dozed back to sleep.

Finally, Charles woke up and seeing the others were asleep, took a third of what was left.

Of course none of the adventurers knew of the other's antics, so, in the morning, they shared the remaining apples, each receiving sixteen. How many apples were in the crate originally?

Alan hid 54, leaving 108. Brain hid 36, leaving 72. Charles hid 24, leaving 48. 48 apples were then available to share in the morning.

To work these numbers out, we start at the end and work backwards.

At the end there were 16 apples each, therefore there were 48 apples.

Charles removed 1÷3 leaving 48, so there must have been 72 apples before he did this.

Brian removed 1÷3 leaving 72, so there must have been 108 apples before he did this.

Alan removed 1÷3 leaving 108, so there must have been 162 apples before he did this. QED.

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