Who stole the N95 face masks

Who stole my surgical face masks?

When we have to stay home in self-isolation, it’s important to exercise the body and mind. Here is a logic puzzle for the mind.

Who stole the precious package of N95  face masks?

Adapted by Israel Zwick, March 31, 2020

Author’s Note: The following story was adapted from Classic Logic Puzzles (Sterling Publishing Co., 2003). The story is entirely fictional. Any resemblance to real persons, places, or events is completely coincidental.

Nancy, a respiratory therapist in a large New York hospital, went into her locker room to put on her personal protective equipment (PPE). She put her package of N95 face masks on the bench and went into the washroom to wash her hands and face according to recommended protocol. When she returned about 2 minutes later, she was shocked to discover that her precious package of face masks was gone. She immediately gathered the four women on the floor who share her locker room and admonished them, “This is not funny. You don’t know what I had to go through to get those face masks.  I went down to the storeroom to look all over and I found one package that fell behind a box of alcohol swabs. Fortunately, the seal wasn’t broken so they were still sterile. This is very serious. I have patients on this floor who are on ventilators and I need to see them. I must have those face masks back right now. I know that one of you took them because you are the only ones on this floor who have a key to the locker room. Give them back right now!”

The four women, Andrea, Barbara, Cynthia, and Denise, responded to her:

Andrea said, “I wasn’t even on the floor, I was in the cafeteria eating breakfast.”

Barbara said, “Cynthia took the masks, I saw her go into the locker room.”

Cynthia responded angrily, “Barbara is lying, it’s not true.”

Denise supported Cynthia, “Cynthia is telling the truth.”

One of the women is lying.  She is guilty. Which one took the face masks?

Hint: Consider that the guilty suspect’s statement is false, and the other statements are true.  Assume that each suspect in turn is guilty. In each case, is this consistent with the statements from the other suspects.

 

Solution:  If you’re bored with nothing to do, keep trying.  If this is contributing to your stress and anxiety, then read the solution below.

Consider that the guilty suspect is lying, everyone else is telling the truth. If we assume that Andrea is guilty, then her statement is false. If so, it means that the other three are telling the truth. However, Barbara says that Cynthia is guilty. If Andrea is guilty, then Andrea and Barbara have both made false statements.  Therefore, Andrea is not guilty.

Assume that Cynthia is guilty. If so, Barbara’s statement, that Cynthia is guilty, is true. However, if Cynthia is guilty, then Cynthia’s and Denise’s statements are both false.  Therefore, Cynthia is not guilty.

Assume that Denise is guilty.  If so, Barbara’s statement that Cynthia is guilty is false.  Yet, we determined that Cynthia is not guilty.  Therefore, Denise is telling the truth and is also not guilty.

Conclusion: Barbara’s statement is false, everyone else is telling the truth.  Barbara took the face masks.

 

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