Answer to A-Bomb-inable Puzzle II (August
(From Boston & Outskirts Mensa Bulletin [BOMB], September 1974)
Lefty and Dopey play for the
1, Sluggers 0
******** AND ******** Something special: John Coons explains how to work the solutions.
There may be some who feel that the puzzle in the last BOMB was too difficult. For those not familiar with this type of puzzle here is how it can be done:
Consider Butchs first and third statements. They must both be either true or false. They cannot both be true. Therefore they are false. The Sluggers are not the Revere team and Butch does not play for the Sluggers. Also, since he lies, Butch does not play for Charlestown.
Consider Flashs second statement. If true, Dopeys statements are true. If true, then Leftys statements are true. If true, then Flash plays for Revere and he lies. Since this is a contradiction, Flashs second statement is false. Dopey does not play for Charlestown. Flash does not play for Charlestown. Flashs fourth statement must also be false. Lefty does always tell the truth.
Since Lefty is truthful, Flash does play for Revere and he always lies. Lefty plays for Brookline. Rocky plays for Medford.
Dopeys third statement is false. Therefore his first statement is false. The Roughnecks are the Brookline team.
The Clippers are not the Revere team (Flash lies). The Thumpers must be the Revere team and Flash plays for the Thumpers. Rocky plays for Medford, and is not a Thumper as his third statement is true. Since Rockys team scored 4 goals against Dopeys team and the Clippers scored only three goals all season, Rocky is not a Clipper. Therefore Medford is the Sluggers and Charlestown is the Clippers.
Rocky plays for the Sluggers and Dopey is on a different team. Since he does not play for Revere or Charlestown, Dopey must play for Brookline. Since Butch does not play for Medford or Charlestown and there are two already present from Brookline, Butch plays for Revere and always lies.
There only remains to find the score in each game.
Since Rockys second statement is false, Roughnecks vs. Thumpers was not a tie game. If Dopeys second statement was true, then the Thumpers other two games were ties, against the Clippers and the Sluggers. We know that the Clippers scored two against the Thumpers (Leftys fifth statement). Therefore the game was a 2-2 tie.
Butchs second statement was false. The Roughnecks did not score more goals against the Clippers than they did against the Sluggers. The Roughnecks scored 0 against the Sluggers (Leftys third statement). The Roughnecks therefore scored 0 against the Clippers. If Dopeys second statement was true, so was his fourth and the Roughnecks scored only three goals all season, all against the Thumpers.
Rockys fourth statement was false. The Clippers did not beat the Roughnecks. The Roughnecks scored 0 goals so the score was 0-0.
Butchs fourth statement was false. The Clippers won at least one game, which must have been against the Sluggers. They scored three goals altogether, two against the Thumpers, so the score against the Sluggers must have been 1-0.
Dopeys and Flashs last statements were both false. The goal ratios of both teams must have been the same. We know the Clippers was 3-2. The Thumpers must be (x + 2 + y)/(x + 2 + 3) = 3/2. Since the total score of any game did not exceed 9, x must = 1 and y = 6. So the Thumpers vs. Sluggers score was 1-1 and the Thumpers beat the Roughnecks 6-3.
Copyright © 1974 Boston Mensa.