Puzzles

We are all about fun mathematics. Try these two puzzles. Send us your thoughts if you like via an email to navajomath@gmail.com.
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    1. (From our friend, @jamestanton):The number 21200 is self-describing: it has 2 zeros,1 one, 2 twos, 0 threes, and 0 fours. How many 5-digits numbers almost like this? How many are correct in 4 of the 5 digits?
    2. Can you plant exactly seven trees, so that there are exactly six rows, each containing exactly three trees?
    3. Is it possible to slice a cube with a straight plane to get a pentagon? Is it possible to slice a cube with a straight plane to get a regular pentagon? Is it possible to slice a cube with a straight plane to get a regular hexagon?
    4. The number \(2015!\) is a really large number. It is equal to $$1 \times 2 \times 3 \times \cdots \times 2014 \times 2015$$ How many zeros does it end with?

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