Three people go to a hotel for the night, it costs $30 for one room, so they split it and each pay $10. The manager realizes he forgot to give them the $5 off discount that week, so he sends a staff member up to their room to give them five dollars.
The staff member thinks to himself "well it's hard to split $5 three ways, so I'll just keep $2 and give each of them $1 and tell them it was a $3 discount!"
So far, each of the three people in the room have paid $10 for the room. After being given $1 each by the staff member, it's as if they had each paid $9, not $10. If you add up the $9 of the three people, and you add in the $2 taken by the staff member, that adds up to &29, not the $30 originally paid.
Where did the $1 go?
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