Boolean Algebra 1
There are 3 boxes labeled A, B and C. Inside each box is a colored plastic chip. One is red, one is white and one is blue. You do not know which chip is in which box. Then, you are told that of the next 3 statements, EXACTLY ONE is true.
a) Box A contains the RED chip
b) Box B does not contain the red chip
c) Box C does not contain the blue chip
You do not know which of the three statements is the true one. From all these statements, determine the color of the chip in each box.
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1 solution
Using some logical reasoning, we can solve this rather easily. To do so, take one of this statement as true and reverse the other two:
Case 1 ( A is true while B and C are false) Box A contains the red chip; Box B contains the red chip; Box C contains the red chip. Conclusion: Both A and B cannot contain the red chip, therefore they both cant be true.
Case 2 ( B is true, A and C are false) Box A does not contain the red chip; Box B does not contain the red chip; Box C contains the blue chip. Conclusion: This doesn't work either: If Box C has the blue chip, then the red chip must be either in A or B but both statements above denied it.
Case 3 ( C is true, A and B are false) Box A does not contain the red chip; Box B contains the red chip; Box C does not contain the blue chip. Finally this works out. Since B has the red chip, blue must be in either A or B. If C does not have the blue chip, A must have the blue and C the white chip. So answer is A= Blue, B=Red, C=White