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Take a Trip With the Teacher
Fun days out go to the highest bidders in this hard Logic Puzzle.
March 3, 2003
By clue 1, Ms. Goldman's excursion got a bid twice as much as the 1st grade teacher's; by clue 5, the trip to the S & O Train Museum brought in twice as much for the school as the 2nd grade teacher's offering; and by clue 7, Ms. Bradley's idea generated twice as much money as the trip to the Aquarium did. Since Ms. Bradley's trip isn't to the S & O Train Museum (clue 2), the teacher offering the train ride is a third teacher to Ms. Bradley and Ms. Goldman. Therefore, there must be some commonality among the three clues with at least one of the three just named appearing as the second teacher in one of the other clues. There are two possible arrangements to satisfy this overlap: either all three clues overlap, giving four teachers, or two clues overlap and one clue stands alone to give all five teachers. In the first case, we would have teacher A's trip 2X teacher B's trip 2X teacher C's trip 2X teacher D's trip (for example, Ms. Goldman's 2X 1st grade teacher's to the S & O Train Museum 2X 2nd grade teacher Ms. Bradley's 2X trip to the Aquarium would be one possible arrangement). By clue 10, if we make teacher D's trip receive the minimum of $150, teacher C's would have brought in $300, teacher B's $600, and teacher A's $1200, a total of $2250 and a conflict with clue 10. We thus have the clues combined so that two of them make teacher A's trip 2X teacher B's trip 2X teacher C's trip and one makes teacher D's trip 2X teacher E's trip and all five are named. If teacher E's trip were the $150 trip in clue 10, teacher D's would have brought in $300--leaving $1350 ($1800 (10) - $450) for the other three teachers. Letting teacher C's trip bring in X money, B's would have brought in 2X and A's 4X, or 7X = $1350. Solving, X would equal $192 and change, 2X $384 and change, and 4X $769 and change--but there is now no way to get the difference of $50 between two trips given in clue 3. So, the $150 was the amount brought in by teacher C's trip, with teacher B's getting a $300 bid and teacher A's a $600 bid. Summing, we get $1050, leaving $750 (10) for the amounts brought in by the trips offered by teachers D and E. With teacher E's bid being X and teacher D's 2X, we have 3X = $750, so that X = $250, Teacher E's trip went for $250 and teacher D's for $500. So, we have the following amounts brought in by the five trips: $600, $500, $300, $250, $150. By clue 3, the trip to the Swishers' basketball game sold for $300, and Ms. Wells got $250 for her offering. The teacher who offered the Swishers outing is the middle one, teacher B, of the arrangement above and can't be the one who is going to take the top bidders to the S & O Museum; she isn't Ms. Goldman (8) and must be Ms. Bradley, with the Aquarium outing then getting a bid of $150 (7). Either Ms. Goldman's or the S & O Train Museum trip got the $600 bid. If it had been the latter, Ms. Goldman's trip would have gone for the $500, with the 1st grade teacher then Ms. Wells (1). By clue 4, the Conemach River rafting excursion would have been Ms. Wells, a contradiction since the 1st grade teacher didn't offer that trip (4). So, Ms. Goldman's trip sold for $600, and Ms. Bradley teaches 1st grade (1). The S & O train ride brought in $500, and Ms. Wells teaches 2nd grade (5). By clue 9, the afternoon at Buster and Davy's was put up for bids by Ms. Wells. Ms. Goldman raised $600 for her idea of a Conemach River raft trip, and the 3rd grade teacher raised $500 (4). Ms. Goldman teaches 5th grade and the one taking her high bidders to the Aquarium teaches 4th (7). By clue 6, Ms. Culpepper teaches 3rd grade and Ms. Lopez 4th. In sum, the teacher-offered excursions raised the following sums for Sunset Beach Elementary School:

  • $600 - Ms. Goldman, 5th grade, Conemach River rafting
  • $500 - Ms. Culpepper, 3rd grade, S & O Train Museum
  • $300 - Ms. Bradley, 1st grade, Swishers basketball game
  • $250 - Ms. Wells, 2nd grade, afternoon at Buster and Davy's
  • $150 - Ms. Lopez, 4th grade, Saturday at the Aquarium

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