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:
Because days is equal to week plus 3days, each of Isabella's circled dates after the first date follows the previousone by days of the week. If she redeems her first coupon on Day , then she will redeem the others, in order, on Days (which is the same day of the week as ) , and (which is the same day of the week ). The only day of the week when she will not redeem a coupon is , so must represent Sunday. Therefore she redeems her first coupon days prior to Sunday, which is Wednesday.
If a coupon is redeemed on a Sunday, then the days on which she redeems a coupon are, in order: Wednesday, Saturday, Tuesday, Friday, Monday, Thursday, Sunday, with this cycle of seven days repeating (assuming an unlimited number of coupons). Note that Sunday appears every seventh day in this list. The days that Isabella redeems her coupons also follow the order of this list, starting with the day she redeems the first coupon. Because Sunday is not a day she redeems a coupon, she redeems her six coupons on the six days starting with Wednesday.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions