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Three men have been sentenced to long terms in prison, but due to over crowed conditions, one man must be released. The warden devises a scheme to determine which man is to be released. He tells the men that he will blindfold them and then paint a red dot or blue dot on each forehead. After he paints the dots, he will remove the blindfolds, and a man should raise his hand if he sees a red dot on one of the other two prisoners. The first man to identify the color of the dot on his own forehead will be release. Of course, the men agree to this. (What do they have to lose?) The warden blindfolds the men, as promised, and then paints a red dot on the foreheads of all three men. He removes the blindfolds and, since each man sees a red dot (in fact two red dots), each prisoner raises his hand. Some time passes when one of the men exclaims, “I know what color my dot is! It's red!" This man is then released. Your problem is to give a proof (a convincing argument) of how the one man deduced that his dot was red. The man could have just guessed but that is not the solution. Hint: Try a proof by contradiction.

Three men have been sentenced to long terms in prison, but due to over crowed conditions, one man must be released. The warden devises a scheme to determine which man is to be released. He tells the men that he will blindfold them and then paint a red dot or blue dot on each forehead. After he paints the dots, he will remove the blindfolds, and a man should raise his hand if he sees a red dot on one of the other two prisoners. The first man to identify the color of the dot on his own forehead will be release. Of course, the men agree to this. (What do they have to lose?) The warden blindfolds the men, as promised, and then paints a red dot on the foreheads of all three men. He removes the blindfolds and, since each man sees a red dot (in fact two red dots), each prisoner raises his hand. Some time passes when one of the men exclaims, “I know what color my dot is! It's red!" This man is then released. Your problem is to give a proof (a convincing argument) of how the one man deduced that his dot was red. The man could have just guessed but that is not the solution. Hint: Try a proof by contradiction.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Here is a story problem. Three men have been sentenced to long terms in prison, but due to over crowed conditions, one man must be released. The warden devises a scheme to determine which man is to be released. He tells the men that he will blindfold them and then paint a red dot or blue dot on each forehead. After he paints the dots, he will remove the blindfolds, and a man should raise his hand if he sees a red dot on one of the other two prisoners. The first man to identify the color of the dot on his own forehead will be release. Of course, the men agree to this. (What do they have to lose?) The warden blindfolds the men, as promised, and then paints a red dot on the foreheads of all three men. He removes the blindfolds and, since each man sees a red dot (in fact two red dots), each prisoner raises his hand. Some time passes when one of the men exclaims, “I know what color my dot is! It's red!" This man is then released. Your problem is to give a proof (a convincing argument) of how the one man deduced that his dot was red. The man could have just guessed but that is not the solution. Hint: Try a proof by contradiction.
Transcribed Image Text:Here is a story problem. Three men have been sentenced to long terms in prison, but due to over crowed conditions, one man must be released. The warden devises a scheme to determine which man is to be released. He tells the men that he will blindfold them and then paint a red dot or blue dot on each forehead. After he paints the dots, he will remove the blindfolds, and a man should raise his hand if he sees a red dot on one of the other two prisoners. The first man to identify the color of the dot on his own forehead will be release. Of course, the men agree to this. (What do they have to lose?) The warden blindfolds the men, as promised, and then paints a red dot on the foreheads of all three men. He removes the blindfolds and, since each man sees a red dot (in fact two red dots), each prisoner raises his hand. Some time passes when one of the men exclaims, “I know what color my dot is! It's red!" This man is then released. Your problem is to give a proof (a convincing argument) of how the one man deduced that his dot was red. The man could have just guessed but that is not the solution. Hint: Try a proof by contradiction.
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