number in Z+is written on the back of each of three cards. The numbers are not necessarily different but the sum of the three numbers is 14. Each card is flipped backwards so that the number cannot be seen by anyone. Carter, Mars, and Mann each select one of the cards, being careful not to let the other two see the number that is on the card. Carter says, after looking at his card, “I know that Mars and Mann have different numbers.” Mars then says, “I already knew that thet hree cards had different numbers.” At this point, Mann confidently exclaims, “I now know all thet hree numbers!” What were the numbers and who had which number?

number in Z+is written on the back of each of three cards. The numbers are not necessarily different but the sum of the three numbers is 14. Each card is flipped backwards so that the number cannot be seen by anyone. Carter, Mars, and Mann each select one of the cards, being careful not to let the other two see the number that is on the card. Carter says, after looking at his card, “I know that Mars and Mann have different numbers.” Mars then says, “I already knew that thet hree cards had different numbers.” At this point, Mann confidently exclaims, “I now know all thet hree numbers!” What were the numbers and who had which number?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 30EQ

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Question

A number in Z+is written on the back of each of three cards. The numbers are not necessarily different but the sum of the three numbers is 14. Each card is flipped backwards so that the number cannot be seen by anyone. Carter, Mars, and Mann each select one of the cards, being careful not to let the other two see the number that is on the card. Carter says, after looking at his card, “I know that Mars and Mann have different numbers.” Mars then says, “I already knew that thet hree cards had different numbers.” At this point, Mann confidently exclaims, “I now know all thet hree numbers!” What were the numbers and who had which number?

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