## Problem of the Day #133: The Three Sophomores
*July 30, 2011*

*Posted by Seungln in : potd , trackback*

Victoria, Veronica and Ivy are playing a number game.

Victoria is thinking of a number that is congruent to $307 \pmod{821}$. Veronica is thinking of a number that is congruent to $283 \pmod{797}$. Ivy is thinking of a number that is congruent to $383 \pmod{877}$. They tell each other what their number is, and, to their surprise, they find out that they all thought of the same number.

If the number they thought of is a positive integer less than $100000000000$, what is the **greatest** number for which this could happen?

## Comments»

Just asking, is there a point to this besides computation?

There unfortunately isn’t too much of non-computation math in this problem. I apologize; it was because I was running out of ideas for good problems. I will try to come up with a better one next time.

I didn’t mean it in a rude way. Coming up with a new problem every few days isn’t easy. I was just wondering whether there was a more clever way to do the problem.