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Bargain Buys
Great bargains = Christmas gifts for dads = a tough Logic Puzzle.
December 19, 2005
By clue 1, the original prices of the five gifts ranged from $30-120. By clue 2, the sale prices ranged from $21-36. By clue 7, the percents off the five gifts ranged from 30-70%. The difference between the gift selling for $30 originally and $21 on sale is $9, or 30% off; these must be the original and sale prices of one gift, since a more than 30% reduction on $30 would result in a final price less than $21. Similarly, the difference between the gift selling for $120 originally and $36 on sale is $84, or 70% off; these must be the original and sale prices of another gift, since a less than 70% reduction on $120 would result in a final price more than $36. So, we have prices of two of the five gifts. By clue 3, the gift Jada bought received a 20% greater discount than the tie and ended up costing $4 than the tie. By clue 3, the tie couldn't have the $120-36 price range or Jada's gift would have cost $40 on sale, no (2). So, either the tie would have the $30-21 range or would be a third gift. Trying the tie as selling for $30 originally and $21 on sale, by clue 3, Jada's buy would have been for $25 on sale with a 50% reduction, so her gift would have cost $50 full price. By clue 4, Lynne's gift cost $50 more originally and $8 more on sale than the gloves. Lynne's gift would have cost the $120-36 or would be a fourth gift to the three named. If Lynne's gift were $120 original and $36 sale price, the gloves would have cost $70 and $28 full and sale price. Adding the four original and four sale prices, we would have $270 and $110--so the fifth gift would have cost $40 original price (by clue 1, the sum of original prices is $310) and $24 on sale (by clue 2, the sum of sale prices is $134). By clue 5, Maria saved $7 more on her gift than the girl who bought the belt saved on hers; there is no way for this clue to work in our arrangement. If Lynne's gift were the fourth one, the gloves couldn't have cost $120 originally or Lynne's gift would have cost $170 (4). If the gloves were Jada's gift, Lynne's gift would have cost $100 full price (4)--a total of $300 for the four gifts and leaving only $10 for the fifth, no (1). So, the gloves would be a fifth gift. By clues 1 and 4, then, Lynne's gift would have cost $80 and the gloves $30 full price and $30 and $22 on sale. However, the $8 reduction on the gloves would be less than 30%, contradicting clue 7. Therefore, the tie did not have the $30-21 price range and is the third gift. Jada's gift doesn't have the $30-21 price range or the tie would have cost $17 on sale (3). If Jada's gift had the $120-36, the tie would have cost $32 on sale with 50% off the original price (3) of $64. By clue 4, Lynne's gift couldn't then be the $30-21 one or the tie, or the gloves would have cost less than $30 originally; Lynne's gift would be a fourth gift. The gloves couldn't be Jada's gift, or Lynne's would have cost $170 originally (4). If the gloves had the $30-21 range, Lynne's gift would have sold for $80 originally and $29 on sale (4). Summing, the four original prices would have totaled $294, leaving $16 (1) for the fifth gift. So, the gloves would be the fifth gift. Summing the three gifts, we would have $214 originally, leaving $96 (1) for Lynne's gift and the gloves. Lynne's gift would have cost $73 and the gloves $23, no (1). Therefore, Jada's gift is the fourth one. By clue 4, Lynne's gift is either the tie, the fifth one, or the one with the $120-36 range. If it were the tie, the least it could have cost on sale would be $29 (2, 4), so that the least Jada's gift could have cost would be $33 (3). Summing, the four sale prices would be at least $119, leaving $15 (2) for the fifth gift, no (2). If Lynne's gift were the fifth one, the gloves couldn't have the $120-36 range (4, 1). If the gloves were Jada's gift, the least the tie could have cost on sale is $21 (2), so that Jada's gift would have cost at least $25 (3) and Lynne's $33 (4)--a total of $136, no (2). If the gloves had the $30-21 range, Lynne's gift would have cost $80 originally and $29 on sale. The three sale prices would total $86, leaving $48 for Jada's gift and the tie (2), which would have cost $26 and $22 respectively (3). Jada would have bought the dress shirt and Nicole the tie (6). However, by clue 5, Maria couldn't have bought the item with the $30-21 range or either the tie or Jada's gift would have been marked down $2, less than the 30% minimum (7); nor could Maria have bought the item in the $120-36 range, a savings of $84, or the tie or Jada's gift would have been marked down $77, making the original price too high. Therefore, Lynne's gift sold for $120 originally and $36 on sale. The gloves would have cost $70 full price and $28 on sale (4). If the gloves were the fifth gift, summing the sale prices would give $85, leaving $49 for Jada's gift and the tie, which would then have cost $26.50 and $22.50 respectively (3). By clue 6, Jada would have bought the dress shirt and Nicole the tie. However, by clue 5, Maria couldn't have bought the item with the $30-21 range or either the tie or Jada's gift would have been marked down $2, less than the 30% minimum (7); nor could Maria have bought the item in the $120-36 range, a savings of $84, or the tie or Jada's gift would have been marked down $77, making the original price too high. So, Jada bought the gloves for $28 after a $42, or 60%, reduction from $70. Then the tie cost $24 on sale after a 40% reduction (3), so it was originally $40. Summing, the original prices total $260 and the sale prices $109, making the fifth gift cost $50 full price (1) and $25 on sale (2). By clue 5, Maria bought the tie, and the belt had the $30-21 range. By clue 6, the dress shirt had the $50-25 and Nicole's gift the $30-21 range. By elimination, Kelly bought her dad a dress shirt and Lynne hers a sweater. In sum, the great sale buys were as follows:

  • Lynne, sweater, $120 - $36
  • Jada, gloves, $70 - $28
  • Kelly, dress shirt, $50 - $25
  • Maria, tie, $40 - $24
  • Nicole, belt, $30 - $21

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