How much wood...? #1
How much wood could a woodchuck chuck if a woodchuck could chuck wood?
Details and Assumptions:
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A "wood" is a tree.
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The wood chuck alternates in choosing whether or not he would like to chuck a tree. For example, if he chucks tree 1, he will not chuck tree 2, and he will chuck tree 3, and so on.
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If a woodchuck decides to chuck a tree, then he will chuck the entire tree.
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Each tree has a volume of 10,000 cubic feet.
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The entire forest has exactly 1,000 trees.
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The woodchuck does not stop until he decides what to do with every single tree in the forest.
What is the total volume of wood, in cubic yards , the woodchuck has chucked at the end of his serial wood-chucking spree? Round your answer to the nearest whole number.
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The answer is 185185.
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1 solution
Out of 1,000 trees, the woodchuck must chuck exactly 500, because if he chucks tree 1, he does not chuck tree 2. This will repeat. That means out of every two trees, one will be chucked, which means the probability of a tree being chucked is 2 1 . Multiplying this probability by 1,000 is equal to 500 .
Now the volume of each tree is 10,000 cubic feet. Multiply this by 500 to get 5,000,000 cubic feet.
But wait, there's more! To get the number of cubic yards, we divide 5,000,000 by 27 since 27 cubic feet can fit into 1 cubic yard. 5,000,000 divided by 27 equals 185,185.185185... . This rounds to 1 8 5 1 8 5 .
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