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Who Ate It (illustration)
FILE No.152Unsolved

Who Ate It

Difficulty ★☆☆about 5 minLogic PuzzleHeadcountTruth and lies
Four people testify that it was eaten by "one," "two," "three," or "four" people. Those who ate lie, and those who did not eat tell the truth.

Case Record

The snack cake is gone. Four friends were there. Those who ate it lie, and those who did not eat it tell the truth. Each of the four says how many people ate the cake.

  • B: "One person ate it."
  • C: "Two people ate it, didn't they?"
  • D: "Three people ate it."
  • E: "Four people ate it."
Your question

Who ate the cake?

Case Files

Diagram

Statements about how many ate the cakeNameStatementB"One person ate it"C"Two people ate it"D"Three people ate it"E"Four people ate it"Rule: those who ate lie; those who did not eat tell the truth.
Diagram

Hints

If you get stuck, open the hints one at a time, in order.

Open hint 1

Are the four statements the same or different?

Open hint 2

At most how many of them can be telling the truth?

Open hint 3

How many people ate?

Solve It

Your question

Who ate the cake?

Choose the answer closest to the truth.

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The Truth

B, C, and E

The answer is "B, C, and E."

What the four say is all different. At most one of them can be telling the truth. If all four were lying, all four would have eaten, so E's "four people" would be true, a contradiction. Therefore exactly one is telling the truth.

If one person tells the truth, three people ate. D, who says "three people," is telling the truth, so D did not eat. The ones who ate are B, C, and E.

Checking each possible number of eatersEatersTruth-tellers(non-eaters)Verdict40✗ E's "four" would then be true31　（D）○22✗ all statements differ: at mostone is true13✗ same reasonOnly D tells the truth, so B, C and E ate it.
Diagram of the solution

Key Points

  • Notice that all the claims conflict
  • Determine the number of truthful people
  • Check against the number who ate

Why people get fooled

Because you start from who ate, and the cases multiply.

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