| I have to admit that I am a confirmed | | | | clue one tells us that the second place finisher had |
| puzzle-head. I love crosswords, acrostics, and | | | | no zeroes, Wayne must have finished in third |
| cryptograms. But I am becoming ever more | | | | place with a total of ten points. We also know |
| intrigued by logic problems. For one thing they | | | | that he is the student who received five different |
| teach you how to become a more attentive | | | | scores because 4+3+2+1+0 equals 10 and clue |
| listener or reader to catch the nuances of | | | | one tells us that only student had five different |
| language that can provide invaluable clues to their | | | | scores.Clue four tells us that Bob's best subject |
| solution. For another, they teach the step-to-step | | | | was writing. This means he got one four only and |
| process of processing information. These are skills | | | | it was in writing. He scored 0 points in gym. Since |
| that are valuable for nearly all reasoning | | | | he scored a total of 12 points, he must have |
| situations.To illustrate the process, the following is | | | | gotten a total of 8 points in Reading, Arithmetic |
| a problem I have composed that will take you | | | | and Art& Poetry. The clue also tells us that he |
| step by step from recognizing the essential | | | | got the same score in two subjects. He only got |
| elements to the final solution. I have not provided | | | | one 4, so he must have gotten 2s or 3s in the |
| a matrix but if you are familiar with the technique | | | | remaining subjects. The only numbers that add up |
| you can construct one yourself from the | | | | to eight are 3, 3 and 2. From clue 2 we know |
| description.I call the problem The Wilson | | | | that Wayne got a 3 in arithmetic and this was a |
| Elementary Subject Olympics. Ed, Bob, Susan, | | | | higher score than Bob. We now know Bob's |
| Anne and Wayne (in no particular order) are five | | | | standing and all of his scores, viz, Reading 3, |
| bright 6th-Grade students attending Wilson School. | | | | Writing 4, Arithmetic 2, Art and Poetry 3, Gym |
| They recently competed in the school's annual | | | | 0.Clue five tells us that Anne got the four in |
| competition. The subjects were: reading, writing, | | | | reading and that she didn't finish last. Bob finished |
| arithmetic, art & poetry, and gym. For scoring | | | | first, Wayne 3rd and Anne 2nd, or 4th. By the |
| purposes, the winner in each subject was | | | | process of elimination, either Susan or Ed must |
| awarded four points; the second place three; | | | | have finished in last place. Please remember that |
| third, two; fourth, one; and fifth, zero. At the end | | | | the last place finisher scored a total of 8 points. |
| of the competition the principal said that it was | | | | Susan has been identified as having seven points |
| the closest competition ever. Each competitor | | | | so far and has at least another for her second |
| was within one point of the next highest finisher. | | | | third place finish.Clue eight says that the third |
| Every competitor got at least one four. From the | | | | place finisher, (Wayne), got a 1 in writing We now |
| following clues, determine the score and order of | | | | know 8 of Wayne's total of 10 points in four |
| finish for each of the students. [N.B. You may | | | | subjects. This means he must have gotten a |
| want to construct two different tables, one with | | | | score of 2 in Reading, the only remaining blank. |
| the names of the students and the subject, the | | | | The rest of the clue tells us that the fourth place |
| other simply the subject and total number of | | | | finisher got a zero in arithmetic. Susan got a 4 |
| points scored in each subject.(1) Only one student | | | | which means that Ed or Ann finished in Fourth |
| got 5 different scores. Bob scored four more | | | | place.Clue nine indicates that Ed got the same |
| points than the last-place finisher. The student in | | | | score in reading and writing. The only scores he |
| second place had no zeroes.(2) Wayne, who did | | | | could have got were ones or zeros. We know |
| not finish fourth or fifth, got a four in gym and | | | | that Anne finished in fourth place, so Ed finished |
| got a higher score than (Bob) in arithmetic.(3) | | | | fifth with a total of 8 points. We already can |
| Susan finished in third place in two subjects but | | | | account for 7 of them so he scored a total of 1 |
| she finished first in arithmetic.(4) Bob's best | | | | point in three subjects. Since he got the same |
| subject was writing and his worst was gym, | | | | score in reading and writing, these must be |
| where he got a zero.(5) Anne got identical scores | | | | zeroes and his one point would be in arithmetic. |
| in writing and gym and a four in reading. She did | | | | By the process of elimination, we now know that |
| not finish last.(6) Ed, Bob, Susan and Anne finished | | | | Susan finished in second place with a total of 11 |
| 1 through 4 in that order in art and poetry.(7) Ed | | | | points. Furthermore Ed, Bob, Anne and Wayne |
| finished fourth in arithmetic, but second in gym. | | | | account for 9 of the 10 points in reading, meaning |
| He also got identical scores in reading and | | | | Susan scored 1.In the arithmetic column we have |
| writing.(8) The third place finisher got a one in | | | | now accounted for all ten points without Anne's |
| writing; the fourth place finisher a zero in | | | | score. Thus, her score must be zero. We're |
| arithmetic.From the above we have more than | | | | almost finished.Clue 5 reads that Anne got identical |
| enough information to solve the problem. For one | | | | scores in writing and in gym. At this point she has |
| thing, we know our students finished within a | | | | a total of 5 points. The identical scores must be |
| point ahead or a point behind their competitors. If | | | | 2s. That leaves he last two numbers to fill in for |
| we add up the total number of possible points for | | | | Susan. She got a 3 in writing and a 1 in Gym.At |
| each category we get 4 plus 3 plus 2 plus 1 or a | | | | long last we have the standings and the scores. |
| total of ten. Since we have five categories with | | | | Bob, first, reading 3, writing 4, arithmetic 2, Art |
| ten points in each we have a total of 50 points. | | | | and Poetry 3 and Gym 0.Susan, second, reading 1, |
| Since each student finished within a point of each | | | | writing 3, arithmetic 4, Art and Poetry 2 and Gym |
| other, the scores will be consecutive integers such | | | | 1. Wayne is third with 2 in reading, 1 in writing, 3 in |
| as 11,12,13,14,15 for example. If you want to, you | | | | arithmetic, zero in art and poetry and 4 in gym. |
| can sit down and experiment to see which five | | | | Anne, who came in fourth, has the following: 4 in |
| integers add up to fifty, but there is a simple | | | | reading, 2 in writing, zero in arithmetic one in Art |
| algebraic formula that will give the number. The | | | | and Poetry and 2 in gym. Last but not least Ed |
| smallest number will be x. The next number will | | | | got a zero in Reading and writing, 1 in arithmetic. 4 |
| be x+1, then x+2, X+3 and x+4. Written out x + | | | | in Art and Poetry and 3 in gym.From a step by |
| (x+1) + (x+2) + (x+3) + (x+4) = 50. 5x+10 = | | | | step approach, we began by finding the total |
| 50. 5x = 40 so x equals 8. The five integers are | | | | number of points available from the clue about |
| 8, 9, 10, 11, 12. Now let's turn to the clues.Clue | | | | the numbers of points scored. After that we |
| number one tells us that Bob had 4 more points | | | | determined Bob finished first with 12 points. Each |
| than the last place finisher. The last place | | | | clue from that point on provided more information |
| competitor scored 8 points. Bob must have | | | | either by statement or inference. What seems at |
| scored a total of twelve, which means he finished | | | | first to be an unintelligible mess gives way to |
| in first place.From Clue number two we know | | | | logical analysis. If you enjoyed it, get yourself a |
| that Wayne did not finish 4th or 5th. Since Bob | | | | logic book and have a ball!The author, John |
| finished first we know Wayne must hsve finished | | | | Anderson, loves puzzles. He has used a number |
| 2nd or third and will have a total of 11 or 10 | | | | of different ones in his novel, The Cellini |
| points.Clue number six gives us four actual scores. | | | | Masterpiece, written under the pen name of |
| Ed got a 4 in art and poetry, Susan 3, Bob 2, and | | | | Raymond John. |
| Anne 1. By inference, Wayne got the zero. Since | | | | |