Problem:
Daphne is visited periodically by her three best friends: Alice, Beatrix, and Claire. Alice visits every third day, Beatrix visits every fourth day, and Claire visits every fifth day. All three friends visited Daphne yesterday. How many days of the next -day period will exactly two friends visit her?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Alice and Beatrix will visit Daphne together every days, so this will happen times. Likewise Alice and Claire will visit together times, and Beatrix and Claire will visit together times. However, each of these counts includes the times when all three friends visit. The number of days that exactly two friends visit is .
The problems on this page are the property of the MAA's American Mathematics Competitions