# Puzzle of the Week: Who Ate the Most Fudge? — Solution

Photo: MonkeySimon/Flickr (CC)

Last week we had you work your logic muscles to solve the conundrum of who ate the most fudge during a friendly game of D&D. Congratulations to Scott for having his correct answer randomly chosen. He’ll receive a \$50 gift certificate from ThinkGeek!

### Puzzle

This week, we have a group of geeks playing D&D and eating fudge. We need to know who ate how much. E-mail your answer to us by Thursday 10 PM EST for your chance to win a \$50 gift certificate to ThinkGeek!

Four geeks and super-logicians were playing their regular D&D Saturday night game at the Logician’s Club headquarters (where they’re all members). One of them had brought the left-overs of a batch of fudge they had made earlier that day. There were 11 pieces, all exactly the same size. The game, as always, was intense, and they ended up eating all of the fudge. Each geek knew how much fudge they had consumed. Nobody knew how much any of the others had eaten, except that each person had eaten at least one piece. At the end of the evening, they wanted to know who had eaten how much, so they agreed to ask only questions to which they didn’t know the answers. Here are the questions:

Albert: Did you eat more pieces of fudge than I did, Betty?
Betty: I don’t know. Did you, Stephanie, eat more fudge than I?
Stephanie: I’m not sure.
Kurt: Aha!

Kurt figured out how many pieces of fudge each geek had eaten. Can you do the same?

### Solution

Kurt: 5 pieces
Stephanie: 3 pieces
Betty: 2 pieces
Albert: 1 piece

Reason:
The inability to answer the question “Did you eat more than me?” can be used to determine “at least so many pieces” for each person. Everyone knows that everyone else had at least one piece. When Albert asked Better if she had more than him, she is unsure. If she only had one piece, the answer would have been absolute (“No, I didn’t”). Consuming only one piece would be at best the same number as him. Her uncertainty indicates she had at least two pieces and not sure if Albert only had one.

Betty then asks the same question to Stephanie. Stephanie is also unsure; however she has heard the previous question & answer. Therefore, Stephanie had more than one piece (same logic as before), PLUS she had more than two pieces. If Stephanie only had two pieces, then her answer to the question would have been “No, I didn’t have more than you.” Stephanie must have had 3 or more pieces.

Kurt, upon hearing these questions / answers is able to solve the problem. Therefore, this information & reasoning must provide him with enough information. Since he knows how much he’s consumed, that Albert had at least one, Betty had at least two, and that Stephanie had at least three, Kurt must have had five pieces to solve the problem at that moment. If only four pieces, he could not have know the solution and consuming six is not possible with only eleven total

With Kurt eating 5 pieces, the rest falls out because of 11 pieces to start with, Stephanie had only 3, Betty had 2, and Albert only 1 piece.

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