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Hints to the PIN (illustration)
FILE No.191Unsolved

Hints to the PIN

Difficulty ★★☆about 5 minLogic PuzzleEliminationPosition
Find the 3-digit PIN from five hints.

Case Record

There are five hints for guessing a 3-digit PIN.

  • 028: One digit is correct and in the right position; another digit is correct but in the wrong position.
  • 809: One digit is correct and in the right position; the other two digits are correct but in the wrong positions.
  • 286: One digit is correct but in the wrong position.
  • 483: One digit is correct but in the wrong position.
  • 265: None of the digits is correct.
Your question

What is the PIN?

Case Files

Diagram

Five cluesGuessClue028One right place; one right digit, wrong place809One right place; the other two right digits, wrong place286One right digit, wrong place483One right digit, wrong place265No right digit
Diagram

Hints

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

Open hint 1

Remove the digits that can't be used, starting from 265.

Open hint 2

In 809, which digits are correct?

Open hint 3

In 809, which one is in the right position?

Solve It

Your question

What is the PIN?

Choose the answer closest to the truth.

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The Truth

908

The answer is "908."

None of the digits in 265 is correct, so 2, 6, and 5 cannot be used. In 809 all three digits are correct, so the digits are 8, 0, and 9.

From 286 and 483, 8 is "correct but in the wrong position," so 8 is not in the middle. In 809 exactly one digit is in the right position, so the PIN is not 809 itself. That leaves 890, 098, and 908. In 028, one digit is correct and in the right position, so either 0 is at the left end or 8 is at the right end. 890 and 098 do not fit this. Only 908 fits all the hints.

Using the clues in turnClueDeduction2652, 6, 5 are out809All three digits right → digits are 8, 0, 9286・4838 is misplaced → not in the middle; not 809 itself0280 first or 8 last → only 908 fits908
Diagram of the solution

Key Points

  • Remove unusable digits first
  • Once the three digits are set, narrow the positions
  • Check against all the hints

Why people get fooled

Because with five hints, you are unsure which to use first.

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