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Chicken Wings

At the China Wing resturant, you can order chicken
wings by the bucket.

The Biggest Bucket O' Wings

is really big!

Figure out how many wings are in it.

If they're removed two at
a time, one wing will be left. If they're removed three at a time, two
wings will remain. If they're removed four, five, or six at a time, then
three, four, and five wings, respectively, will remain. If they're taken
out seven at a time, no wings will be left over.
What's the smallest possible number of wings that could
be in the bucket? How do you know?

Show your work and justify your answer.