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?
Statement 2 is a little ambiguous. I interpreted it as 'Bobby and Billy have the same color which is different from Betty's color' and 'Betty and Bobby purchased the same item which is different from Billy's color'.
With that interpretation, The following can be deduced from the statements:
Betty: brown bike
Bobby: beige bike
Billy: beige ball/balloon
Brian: blue ball/balloon
If clue 6 read "A balloon was not purchased by Brian", then the solution is:
Betty: brown bike
Bobby: beige bike
Billy: beige balloon
Brian: blue ball
If clue 6 read "A balloon was not purchased by Billy", then the solution is:
Betty: brown bike
Bobby: beige bike
Billy: beige ball
Brian: blue balloon
Solution
