Problem:
Isabella has coupons that can be redeemed for free ice cream cones at Pete's Sweet Treats. In order to make the coupons last, she decides that she will redeem one every days until she has used them all. She knows that Pete's is closed on Sundays, but as she circles the dates on her calendar, she realizes that no circled date falls on a Sunday. On what day of the week does Isabella redeem her first coupon?
Answer Choices:
A. Monday
B. Tuesday
C. Wednesday
D. Thursday
E. Friday
Solution:
Let us go through the answer choices. If she starts on Monday, her next day is Thursday, and the day after is Sunday. If we start with Tuesday, the next day is Friday. The day after is Monday, which as we know from above will hit Sunday in more days. If we start with Wednesday, the next day is Saturday. The day after is Tuesday, which we know hits Sunday only after more iterations. Therefore, if we start with Wednesday, we loop through iterations without hitting Sunday. Thus, the correct answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions