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:

1. Betty did not purchase a balloon.

2. Bobby and Billy purchased the same color item, which was not brown. Betty and Bobby purchased the same item.

3. Betty thought it best to purchase a brown item.

4. Brian is the only one who purchased both his item and his color.

5. 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?