Luke has red marbles and blue marbles in a bag. If he chooses a marble at random, the probability that he will choose a blue marble is . Luke adds 5 blue marbles to the bag and removes 5 red marbles. If he chooses a marble at random, the probability that he will choose a blue marble is now . How many marbles are in the bag?
, 2012
Pick one
Solution
If either Chris or Mark says, “Tomorrow, I will lie." on a day that he tells a lie, then it actually means that tomorrow he will tell the truth (since he is lying).
This can only occur when he lies and then tells the truth on consecutive days.
For Chris, this only happens on Sunday, since he lies on Sunday but tells the truth on Monday.
For Mark, this only happens on Thursday, since he lies on Thursday but tells the truth on Friday.
Similarly, if either Chris or Mark says, “Tomorrow, I will lie." on a day that they tell the truth, then it means that tomorrow they will lie (since they are telling the truth).
This can only occur when they tell the truth and then lie on consecutive days.
For Chris, this only happens on Thursday, since he tells the truth on Thursday but lies on Friday.
For Mark, this only happens on Monday, since he tells the truth on Monday but lies on Tuesday.
Therefore, the only day of the week that they would both say, “Tomorrow, I will lie.", is Thursday.
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