Personal Comment: I think this is good because it does not need paper math.
Band lineup Enigma
What we know:
The school's band has lined up in rows of 4.
There is one person in the end who does not have partner, so the director says to line up with 3 in a row.
There is still somebody in the end with no partners so the director now says to have just 2 people in each row.
Still, there is the lonely band member with no partner.
Finally, the director orders everyone to line up in rows of five.
Finally, the lonely member gets to line up and no body is left behind with no partners.
Enigma: How many people are in the band?
Solution: 25
25 is divisible by 5 but not 4, 3, or 2.
See who got this right
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