How Logic Puzzles Can Help You Become a Better Problem Solver

I have to admit that I am a confirmedclue one tells us that the second place finisher had
puzzle-head. I love crosswords, acrostics, andno zeroes, Wayne must have finished in third
cryptograms. But I am becoming ever moreplace with a total of ten points. We also know
intrigued by logic problems. For one thing theythat he is the student who received five different
teach you how to become a more attentivescores because 4+3+2+1+0 equals 10 and clue
listener or reader to catch the nuances ofone tells us that only student had five different
language that can provide invaluable clues to theirscores.Clue four tells us that Bob's best subject
solution. For another, they teach the step-to-stepwas writing. This means he got one four only and
process of processing information. These are skillsit was in writing. He scored 0 points in gym. Since
that are valuable for nearly all reasoninghe scored a total of 12 points, he must have
situations.To illustrate the process, the following isgotten a total of 8 points in Reading, Arithmetic
a problem I have composed that will take youand Art& Poetry. The clue also tells us that he
step by step from recognizing the essentialgot the same score in two subjects. He only got
elements to the final solution. I have not providedone 4, so he must have gotten 2s or 3s in the
a matrix but if you are familiar with the techniqueremaining subjects. The only numbers that add up
you can construct one yourself from theto eight are 3, 3 and 2. From clue 2 we know
description.I call the problem The Wilsonthat 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 fivestanding 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 annual0.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 scoringfirst, Wayne 3rd and Anne 2nd, or 4th. By the
purposes, the winner in each subject wasprocess 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 endthe last place finisher scored a total of 8 points.
of the competition the principal said that it wasSusan has been identified as having seven points
the closest competition ever. Each competitorso 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 theplace finisher, (Wayne), got a 1 in writing We now
following clues, determine the score and order ofknow 8 of Wayne's total of 10 points in four
finish for each of the students. [N.B. You maysubjects. This means he must have gotten a
want to construct two different tables, one withscore of 2 in Reading, the only remaining blank.
the names of the students and the subject, theThe rest of the clue tells us that the fourth place
other simply the subject and total number offinisher got a zero in arithmetic. Susan got a 4
points scored in each subject.(1) Only one studentwhich means that Ed or Ann finished in Fourth
got 5 different scores. Bob scored four moreplace.Clue nine indicates that Ed got the same
points than the last-place finisher. The student inscore in reading and writing. The only scores he
second place had no zeroes.(2) Wayne, who didcould have got were ones or zeros. We know
not finish fourth or fifth, got a four in gym andthat 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 butaccount for 7 of them so he scored a total of 1
she finished first in arithmetic.(4) Bob's bestpoint 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 scoreszeroes and his one point would be in arithmetic.
in writing and gym and a four in reading. She didBy the process of elimination, we now know that
not finish last.(6) Ed, Bob, Susan and Anne finishedSusan finished in second place with a total of 11
1 through 4 in that order in art and poetry.(7) Edpoints. 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 andSusan scored 1.In the arithmetic column we have
writing.(8) The third place finisher got a one innow accounted for all ten points without Anne's
writing; the fourth place finisher a zero inscore. Thus, her score must be zero. We're
arithmetic.From the above we have more thanalmost finished.Clue 5 reads that Anne got identical
enough information to solve the problem. For onescores in writing and in gym. At this point she has
thing, we know our students finished within aa total of 5 points. The identical scores must be
point ahead or a point behind their competitors. If2s. That leaves he last two numbers to fill in for
we add up the total number of possible points forSusan. She got a 3 in writing and a 1 in Gym.At
each category we get 4 plus 3 plus 2 plus 1 or along last we have the standings and the scores.
total of ten. Since we have five categories withBob, 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 eachwriting 3, arithmetic 4, Art and Poetry 2 and Gym
other, the scores will be consecutive integers such1. Wayne is third with 2 in reading, 1 in writing, 3 in
as 11,12,13,14,15 for example. If you want to, youarithmetic, zero in art and poetry and 4 in gym.
can sit down and experiment to see which fiveAnne, who came in fourth, has the following: 4 in
integers add up to fifty, but there is a simplereading, 2 in writing, zero in arithmetic one in Art
algebraic formula that will give the number. Theand Poetry and 2 in gym. Last but not least Ed
smallest number will be x. The next number willgot 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 arenumber of points available from the clue about
8, 9, 10, 11, 12. Now let's turn to the clues.Cluethe numbers of points scored. After that we
number one tells us that Bob had 4 more pointsdetermined Bob finished first with 12 points. Each
than the last place finisher. The last placeclue from that point on provided more information
competitor scored 8 points. Bob must haveeither by statement or inference. What seems at
scored a total of twelve, which means he finishedfirst to be an unintelligible mess gives way to
in first place.From Clue number two we knowlogical analysis. If you enjoyed it, get yourself a
that Wayne did not finish 4th or 5th. Since Boblogic book and have a ball!The author, John
finished first we know Wayne must hsve finishedAnderson, loves puzzles. He has used a number
2nd or third and will have a total of 11 or 10of 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, andRaymond John.
Anne 1. By inference, Wayne got the zero. Since