In how many ways can the numbers 1 through 5 be entered once each into the five boxes below so that all the given inequalities are true?

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Guest Nov 13, 2022

#2**+1 **

*In how many ways can the numbers 1 through 5 be entered once each into the five boxes below so that all the given inequalities are true?*

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Firset, consider the middle box.

It can be only a 1, because that's the only number in the list that there are four others larger than it.

So, for the middle box, there can be only a 1. After that, the rest is easy.

5 > 4 > 1 < 2 < 3

5 > 3 > 1 < 2 < 4

3 > 2 > 1 < 4 < 5

4 > 2 > 1 < 3 < 5

These are **FOUR** ways to do it. Maybe you can think of some others that I missed. But there aren't 44, that's for sure.

**.**

Guest Nov 13, 2022

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edited by Guest Nov 13, 2022

edited by Guest Nov 13, 2022

edited by Guest Nov 13, 2022