UT Math Club Problem of the Month
October 2012
Problem I Find all integer solutions of
1
1
1
3
+
−
= .
2
n m mn
4
Problem II Ali Barber, the carpet merchant, has a rectangular piece of carpet
whose dimensions are unknown. Unfortunately, his tape measure is
broken and he has no other measuring instruments. However, he finds
that if he lays it flat on the floor of either of his storerooms, then each
corner of the carpet touches a different wall of that room. If the two
rooms have dimensions of 38 feet by 55 feet and 50 feet by 55 feet, what
are the carpet dimensions?
Submission Deadline: ??
1