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.

Name: Writing and Proof: Here is a story problem.Three men have been sentenc
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Description: Writing and Proof: Here is a story problem.Three men have been sentenced to long terms in prison, butdue to over crowed conditions, one man must be released.The warden devises a scheme to determine which man is tobe released. He tells the men that he

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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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Question

Writing and Proof:

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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