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?
This problem is not solvable. All of the previous posts have been assuming a clue which is not present. Namely, that all three items were purchased.
Given the clues present, the following can be deduced:
Betty: Brown Bike
Bobby: Beige Bike
Billy: Something Beige
Brian: Something Blue
The missing clue will not make this problem solvable. If it read "A balloon was not purchased by Brian", we would be left with the fact that Brian purchased a Blue Ball. We know, then, that Billy did not purchase a ball, but that leaves the options of Beige Balloon, and Beige Bike, both of which are permissible by the previous statements.
If the missing clue named Billy as the non-balloon-purchasing child, then Billy is restricted to buying a Bike or a Ball. Both of these options are valid from the statements we are given, as there is no prohibition against Beige Balls or Beige Bikes. Only if Billy purchased a Ball would we have a solution for Brian. However, we have no way to know that Billy bought a ball simply because he did not buy a balloon.
-- Alec
Not solvable
