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Magician's Solution From Math Olympiad (Math Chat)

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Author:Frank Morgan, MAA Online
Description: Answer to the Challenge from the 2000 International Math Olympiad: A magician has one hundred cards numbered 1 to 100. He puts them into three boxes, a red one, a white one and a blue one, so that each box contains at least one card. A member of the audience selects two of the three boxes, chooses one card from each and announces the sum of the numbers on the chosen cards. Given this sum, the magician identifies the box from which no card has been chosen. How many ways are there to put all the cards into the boxes so that this trick always works? (Two ways are considered different if at least one card is put into a different box.)

Levels: High School (9-12), College
Languages: English
Resource Types: Articles
Math Topics: Permutations/Combinations

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