Logical Larry was upset to learn that his recent submission to a logic problem magazine had multiple solutions. As it turns out, the magazine editor accidentally omitted one of his clues.
Here is the clue as it was printed:
Four children (Betty, Bobby, Billy, and Brian) enter a store selling bikes, balls, and balloons, each of which come in blue, brown, or beige.
From the clues below, determine what each child purchased:
- Betty did not purchase a balloon.
- Bobby and Billy purchased the same color item, which was not brown. Betty and Bobby purchased the same item.
- Betty thought it best to purchase a brown item.
- Brian is the only one who purchased both his item and his color.
- A brown ball was not purchased. Neither was a blue bike.
The missing clue should have read, "A balloon was not purchased by _________" However, Larry cannot remember what should be in the blank to make the problem solvable.
What should be in the blank?
The missing clue should NOT read "A balloon was not purchased by Brian" or " A balloon was not purchased by Billy", but rather "A balloon was not purchased by anyone of these kids!"
From 1,3 and 5 we know Betty bought a brown bike.
From 2 we now know Bobby also has a bike and since Bobby and Billy have the same color item and (4) Brian has a different color than all of them and (5) there is no blue bike, Bobby bought a beige bike.
Now Billy bought something beige and Brian bought something blue and Brian bought something no one else did. If the missing clue reads Brian then he bought the ball but Billy bought either the bike or the balloon. If the missing clue reads Billy then he could have bought the ball while Brian bought the balloon or Billy could have bought the bike and Brian could have bought the balloon or ball.
After re-reading the problem we see Larry wrote what should be in the blank. So if we make the clue "A balloon was not purchased by anyone" then Brian bought a ball and Billy bought a bike and the final purchases are as follows:
Betty: brown bike; Bobby: beige bike; Billy: biege bike; Brian: blue ball.
Edited on April 28, 2004, 10:22 am
Two options
