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# Batcave

## Question

A number of bats are in a cave.

• 4563 bats can see out of their left eye.

• 3645 bats can see out of the right eye.

• At least 5436 bats cannot see out of their left eye.

• At least 6354 bats cannot see out of their right eye.

What is the smallest number of bats that can be in the cave?

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And the 9999 is prolly an obviously wrong answer ?

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5534

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Could the answer be 0 bats--since nothing was said in the subsequent lines about the bats mentioned being in the cave?

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9999. No matter how I try to pair them up I have to have 3645 with a good right eye and at least 6354 with a bad right eye (or 4563 with a good left eye and at least 5436 with a bad left eye). Each pair of numbers adds to 9999.

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Could the answer be 0 bats--since nothing was said in the subsequent lines about the bats mentioned being in the cave?

I actually was thinking down the same lines, except I was thinking "2"...because the question states there are bats (note the plurality) in the cave...and then asks how many bats are in the cave...it doesn't necessarily say that the bats with descriptions about their eyes are the ones in the cave. Therefore, I'd say 2 is a valid answer...

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Wouldn't the answer be all of them?

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The answer is one. The question asked is what is the smallest number of bats in the cave. It does not matter that the bats are blind, myopic or wearing eye patches! The answer is one because that it is one more than none. As for the answer being zero i would point out that the question asks about the number of bats IN the cave and semantically this rules out a null equation.

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You guys are funny.

9999

The question wasn't very hard or deceptive, but I thought it was interesting because, you only need to add the mutually exclusive sets of bats and realize that the left eye and right eye of each bat are independent.

This makes the problem straightforward if you stay focused on the important factors, however, I thought that people might make assumptions about correlating blindness in left eyes and right eyes, or attempt to calculate all the possible ways left eyes can go with right eyes with a large number of bats...etc

Out of the box solutions are technically valid, though maybe next time, I'll try to word questions in ways that make it harder to answer in this manner.

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