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Coupons
Coupons save money.
March 21, 2005
From the introduction, the coupons Stan Cash used were for whole cents, with no two being for the same refund. By clue 2, the coupon for Cheerios wasn't cut from a magazine. In clues 4 and 7, then, four different coupons are named: the one for Cheerios was for twice as much as the in-store one and the one from a magazine was for twice as much as the Bounty paper towels coupon. The Bounty coupon didn't come from the Sunday paper (clue 5), so the coupon cut from the Sunday paper was either for Cheerios or was the fifth one cashed in addition to the four in clues 4 and 7. Trying the Sunday paper coupon being for Cheerios, by clue 6, one coupon was worth $1.00. If the Sunday paper coupon for Cheerios were the $1.00 coupon, then both the coupon from the mailer (1) and the in-store coupon (4) would have been worth .50, contradicting the introduction. If the in-store coupon had been for $1.00, the Sunday paper Cheerios coupon would have been for $2.00 (4) and the coupon from the mailer then for $1.50 (1)--a total of $4.50 and above the total $3.90 Stan saved (introduction). If the Bounty coupon had been for $1.00 and the magazine coupon then for $2.00 (7), the Bounty coupon couldn't have come from the mailer or the Sunday paper Cheerios coupon would have been for $1.50--a total of $4.50 and too much. The mailer coupon would have been the fifth one. Letting the in-store coupon be worth X, the Sunday paper Cheerios one would be for 2X (4), and the mailer coupon for 2X - .50 (1), a total of 5X - .50 equalling .90. Solving, 5X = 1.40 or X = .28. The in-store coupon would have been for .28, the Cheerios one for .56, and the mailer one for .06--but there is no way clue 3 can work given these numbers. If the magazine coupon had been for $1.00 and the Bounty one for .50 (7), the Bounty coupon couldn't have come from the mailer or the Sunday paper Cheerios coupon also would have been for $1.00 (1). So, the fifth coupon would have come from the mailer. Letting the in-store coupon be worth X, the Sunday paper Cheerios one would be for 2X (4) and the mailer coupon for 2X - .50 (1), a total of 5X - .50 equalling 2.40 (3.90 - 1.50 for the magazine and Bounty coupons). Solving, 5X = 2.90 or X = .48. The in-store coupon would have been for .48, the Cheerios one for .96, and the mailer one for .46--but there is no way clue 3 can work given these numbers. So, if the Cheerios ad had come from the Sunday paper, the fifth coupon would be for $1.00. If it were the one from the mailer, the Cheerios coupon would have been for $1.50 (1) and the in-store one for .75 (4), a total of $3.25. Then the X for Bounty plus 2X for the magazine coupon would equal .65, or the Bounty coupon for .2167 and the magazine one for .4333, contradicting the whole cents in the introduction (and clue 3). So the Bounty coupon would have come from the mailer. Making the in-store coupon worth X, the Cheerios coupon in the Sunday paper would be for 2X (4), the Bounty one from the mailer worth 2X - .50 (1), and the one from the magazine for 4X - 1.00. Summing, 9X - 1.50 = 2.90 or X equals .489, contradicting the introduction. Therefore, the coupon cut from the Sunday paper is the fifth to the four in clues 4 and 7. If it were the one for $1.00 (6), the one from the mailer would be worth .50 (1); the one from the mailer couldn't then be for Bounty or the magazine coupon would also have been for $1.00 (7), so it would be for Cheerios. The in-store coupon would have been for .25 (4)--a total of $1.75, leaving $2.15 for clue 7. However, X for Bounty and 2X for the magazine coupon make X worth .717, no (intro). If the Bounty coupon were for $1.00, the magazine one would be for $2.00. The Bounty coupon couldn't be from the mailer or the Sunday paper coupon would have been for $1.50, adding to $4.50. The Cheerios coupon would have come from the mailer. Letting the in-store coupon be for X, the Cheerios one would have been worth 2X (4) and the Sunday paper one for 2X + .50 (1), so that 5X + .50 would equal .90 and X would be worth .08. So the in-store coupon would have been for .08, the Cheerios one for .16, and the Sunday paper one for .66--but clue 3 cannot work. If the magazine coupon were worth $1.00, the Bounty one would have been for .50 (7). The Bounty coupon couldn't have come from the mailer or the Sunday paper coupon would also have been worth $1.00 (1), so the Cheerios coupon would have come from the mailer. Letting the in-store coupon be for X, the Cheerios one would have been worth 2X (4) and the Sunday paper one for 2X + .50 (1), so that 5X + .50 would equal 2.40 and X would be worth .38. So the in-store coupon would have been for .38, the Cheerios one for .76, and the Sunday paper one for 1.26--but again clue 3 cannot work. If the in-store coupon had been the one for $1.00, the Cheerios coupon would have saved Stan $2.00 (4). The Cheerios coupon then couldn't have come from the mailer or the Sunday paper one would have been for $2.50--a total of $5.50. The Bounty one would have come from the mailer. Letting it be for X, the one in the Sunday paper would have been for X + .50 (1) and the one in the magazine for 2X (7), a total of 4X + .50 and equal to .90. Solving, X would be .10, so that the Bounty coupon would have been for .10, the one in the Sunday paper for .60, and the one from the magazine for .20--numbers that contradict clue 3. So, the Cheerios was for $1.00, with the in-store one then worth .50 (4). If the Bounty coupon were from the mailer, then it would have been worth X, the one in the Sunday paper would have been for X + .50 (1) and the one in the magazine for 2X (7), a total of 4X + .50 and equal to 2.40. Solving, X would be .475, a fraction and conflict with the introduction. So, the Cheerios coupon came from the mailer and the Bounty coupon from a previous purchase. The Sunday paper coupon saved Stan $1.50 (1). Letting the the Bounty coupon be worth X and the one in the magazine worth 2X (7), 3X would equal .90; solving, X would be .30. The Bounty coupon was for .30 and the magazine one for .60. By clue 3, the magazine coupon was for Tide detergent. Finally, by clue 8, the Sunday paper coupon was for Red Baron pizza and the in-store one for Kraft Italian salad dressing. In sum, Stan saved money as follows:

  • Red Baron pizza, Sunday paper, $1.50
  • Cheerios cereal, mailer, $1.00
  • Tide detergent, magazine, $.60
  • Kraft dressing, in-store, $.50
  • Bounty paper towels, previous purchase, $.30

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