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## The Total is 14, Part III

Logic puzzles require you to think. You will have to be logical in your reasoning.

 Puzzle ID: #30010 Fun: (2.7) Difficulty: (2.76) Category: Logic Submitted By: tsimkin Corrected By: Winner4600

Mr. Simkin, the new math teacher at school, was impressed by his students' ability to solve logic puzzles. He pulled aside three more students, and handed them each a sealed envelope with a number written inside. He told them that they each have a positive integer, and the sum of their numbers was 14.

Manny, Moe, and Jack each opened their envelopes. Mr. Simkin asks Manny if he knows anything about the numbers the other two are holding, and Manny says, "I know that Moe and Jack are holding different numbers."

Moe answers, "IN THAT CASE, I know that all three of our numbers are different."

Jack thinks for a bit, and then says, "Now I know all of our numbers."

Mr. Simkin turns to the class and asks if anyone in the class knows the numbers. Gretchen's hand shoots up into the air, and after waiting for a while to see if anyone else will get the answer, Mr. Simkin calls on Gretchen.

What numbers does she say they each are holding?

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