# KEYS

**Discrete Mathematics**Level 2

Allan, Allen, and Ellen collects keys.

Allan collected 5 keys more than Allen, but Allen gathered 5 keys less than Ellen.

All in all, they have 34 keys.

Allan collected 5 keys more than Allen, but Allen gathered 5 keys less than Ellen.

All in all, they have 34 keys.

Allen, who has the least number of keys, decides to put his keys in a key ring.

In how many ways can he arrange his keys in a key ring?

Note: Reflections and rotations are considered identical.

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