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, Alex woke up and decided to hide some of the apples and hid a third, then promptly fell asleep again.
Blake woke up shortly after and also decided to hide a third of the remaining apples and then also dozed back to sleep.
Finally, Charlie 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?
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How many apples were left after Charlie had taken some?
Alex hid 54, leaving 108.
Blake then hid 36, leaving 72.
Charlie then hid 24, leaving 48 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 in total.
Charlie removed one third leaving 48, so there must have been 72 apples before.
Blake removed one third leaving 72, so there must have been 108 apples before.
Alex removed one third leaving 108, so there must have been 162 apples before.
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