### Instruction: On a Tuesday, a magician said, ``I made my wife disappear 31 days ago.'' What day of the week did he make her disappear?### Response: I need to find the day of the week that is 31 days before a Tuesday.
I know that a week has 7 days, so I can use modular arithmetic to find the remainder when 31 is divided by 7.
31 divided by 7 is 4 with a remainder of 3.
That means that 31 days ago was 3 days before Tuesday, which is Saturday.
So the magician made his wife disappear on a Saturday.