Bowling League
Logic puzzles require you to think. You will have to be logical in your reasoning.
Joyce and her four best friends bowl together on a team named the Alley Cats. The team played a great game last Friday as each woman's score was higher than her average. Can you find each bowler's full name and her Friday night score?
Given:
Scores  170, 175, 195, 210, 230
First Names  Amy, Evelyn, Hillary, Joyce, Opal
Last Names  Marin, Peterson, Rielly, Shapiro, Webster
Clues:
#1) Hillary, whose average is 197, isn't Ms. Webster
#2) Opal scored exactly 20 more points than Ms. Shapiro
#3) Ms. Rielly (who isn't Evelyn), scored lower than Opal's average
#4) Amy's score was higher than Ms. Peterson's
#5) Opal is NOT Ms. Marin and neither woman scored 230 points.
HintMake a list of one set of givens and list another set of givens that would correspond to them... i.e. (first names)  (last names)
Amy  Marin, Peterson, Rielly, Shapiro, Webster
Evelyn  Marin, Peterson, Rielly, Shapiro, Webster, etc.
Cross off what you know is NOT the correct answer from the clues, and when you find out a last name that fits a first name circle it, or write the full name on the piece of paper in a different section to keep track. Do the same with the other correlations that can be surmised by looking at the clues:
(last names)  (bowling scores)
(first names)  (bowling scores)
Keep in mind that for example, if you find a last name for a first name, the other first names can NOT have that last name, so that gives you another answer to mark off to narrow the correct answer down.
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Answer
Joyce Rielly  170
Evelyn Shapiro  175
Amy Webster  230
Hillary Marin  210
Opal Peterson  195
**Clue #1: We know Hillary isn't Ms. Webster, so you can cross that off immediately. We also know that Hillary's bowling average is 197. The problem states that it was a good night because each lady scored higher than her average. We know then, that Hillary's average must be either 210 or 230. Cross off the others for Hillary.
**Clue #2: Opal scored 20 more points than Ms. Shapiro. Looking at the scores, there are 2 sets of the numbers that have differences of 20. 175 ; 195 and 210 ; 230. So for Opal and Ms. Shapiro, you can immediately mark off the 170 score. Also, Opal can NOT be Ms. Shapiro.
**Clue #3: Ms. Rielly is NOT Evelyn, so cross off Rielly on Evelyn's list. Rielly scored lower than Opal. This means that Opal cannot have the lowest score, which was crossed off in the last clue, and Rielly can NOT have the highest score. So cross off the 230 on Rielly's list. Also, if it says Rielly scored lower than Opal, we can assume Opal is NOT Ms. Rielly...mark it off.
**Clue #4: If Amy's score was higher than Ms. Peterson's, then Amy cannot have the lowest score (170) and Ms. Peterson cannot have the highest score (230). Cross them off. Here as well, we can assume that if they have different scores, Amy can NOT be Ms. Peterson.
**Clue #5: Opal is NOT Ms. Marin, neither scored 230 points. Cross them off. If Opal did not score 230 points, then the 20 point difference is not the 210 ; 230. So we know that Opal and Ms. Shapiro's scores are 195 and 175, respectively. Since we know Shapiro has a 175, any of the first names that have 175 crossed off can NOT be Shapiro, therefore Hillary can NOT be Ms. Shapiro...mark it off. Also note that Ms. Webster scored 230.
*********Once we know that Opal's score is 195, we know that Rielly scored lower than that. So Rielly's score is either 170 or 175. Shapiro's score is 175, so we know that Rielly's score is 170. First names with 170 marked off already can NOT have a last name of Rielly. SO mark off Rielly on Amy's, Hillary's, and Opal's list. We now see that the full name is Joyce Rielly with a score of 170. Now you have the first complete section of the answer. Also, we know Opal is NOT Ms. Marin, so you can cross off 195 from Ms. Marin's score list. Now we know Marin scored 210. That leaves Peterson with 195. Opal is Ms. Peterson. We know that Amy scored higher than Ms. Peterson, who scored 195. So Amy could only have scored a 210 or 230. Marking 175 off Amy's list shows you Evelyn has 175. which makes her Ms. Shapiro. Marking Webster off of Opal's list, leaves Amy as Webster which in turn leaves Hillary as Marin.
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