Tokens in a bag
Ms.Q. places tokens numbered 1 through 5 in a bag. The tokens feel exactly the same. Students pull tokens from the bag without looking into the bag.
Lisa and Wendy each pull out two tokens. Ms.Q. asks Wendy, “Is the number of the token left in the bag odd or even?”
Wendy looks at her tokens and says, ”I don’t know.”
Ms.Q. asks Lisa, “Do you know?”
Lisa looks at her tokens and says, “I didn’t know before Wendy said she didn’t know but now I know.”
Is the numbered token left in the bag odd or even?
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1 solution
Since there are two even and three odd tokens, the only way Wendy or Lisa could know the answer immediately is if one of them had both even tokens.
In addition, if Lisa had exactly one even token, she would not have gained new information from Wendy stating that she doesn‘t know the answer (since Lisa would already know she doesn‘t have both even tokens).
Therefore, Lisa has two odd tokens, and Wendy‘s statement indicates to her that there is an even token left over.