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