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Predicting the Ranking (illustration)
FILE No.163Unsolved

Predicting the Ranking

Difficulty ★★☆about 5 minLogic PuzzleAssumptionsContradictions
Runners A to D. Each of three people's predictions has exactly one of its two parts correct.

Case Record

Runners A, B, C, and D ran a race. There were no ties. Three people predicted the ranking, and in each prediction exactly one of the two parts was correct.

  • Ken's prediction: "A is 1st. B is 2nd."
  • Miki's prediction: "D is 2nd. C is 3rd."
  • Taku's prediction: "B is 3rd. C is 1st."
Your question

What is the ranking? (1st to 4th)

Case Files

Diagram

Predictions for runners A–D (exactly one part of each is right)PredictorPredictionKenA is 1st. B is 2ndMikiD is 2nd. C is 3rdTakuB is 3rd. C is 1stNo ties. What is the finishing order?
Diagram

Hints

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

Open hint 1

Start with the case where Ken got "A is 1st" right.

Open hint 2

Each prediction has exactly one correct part.

Open hint 3

Decide who is 3rd.

Solve It

Your question

What is the ranking? (1st to 4th)

Choose the answer closest to the truth.

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The Truth

A, D, B, C

The answer is "A, D, B, C."

If Ken is right that A is 1st, then B is not 2nd. In Taku's prediction, C being 1st is wrong (A is 1st), so B being 3rd is right. In Miki's prediction, D being 2nd is right and C being 3rd is wrong. This gives A, D, B, C.

None of the other rankings in the choices satisfies "exactly one correct in each prediction."

1st to 4th: A, D, B, CPredictionFirst partSecond partHitsKenA 1st ✓B 2nd ✗1MikiD 2nd ✓C 3rd ✗1TakuB 3rd ✓C 1st ✗1Each prediction has exactly one right part.
Diagram of the solution

Key Points

  • Start from one assumption and look for a contradiction
  • Use the condition "exactly one"
  • Check all three predictions at the end

Why people get fooled

Because you try to consider all the predictions at once and get confused.

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