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Kode #178: hints & solution

Here's the clue board for Kode #178. Start with the spoiler-free hints. If you're still stuck, the full step-by-step solution is below, hidden until you open it.

The clue board

Each row is a guess that's already been graded. ▲ means a right digit in the right spot; ● means a right digit in the wrong spot.

  • 17239▲1●1
  • 27836▲0●1
  • 34298▲0●2
  • 42016▲0●0
  • 53591▲0●3

Spoiler-free hints

  • Exactly one of the four digits is even.
  • The four digits add up to 21.
  • 2 of the digits are 5 or higher.

Try the hints first. The solution below walks through every deduction.

Step-by-step solution

Every Kode can be cracked by pure deduction, with no guessing. This board falls in 9 logical steps. Open the solution to follow them one at a time.

Show the solution · reveals the code

When a row "rules out" a position, it shows that digit there but its ▲ marks are already used up (or it has none), so the digit can't sit there.

  1. Row 4 (2 0 1 6) has no marks at all, so 2, 0, 1, and 6 are not in the code.
  2. Row 5 (3 5 9 1) has 3 marks still unexplained, and only 3 digits are left undecided: 3, 5, and 9. So all of them are in the code.
  3. Row 1 (7 2 3 9) has 2 marks, already accounted for by 3 and 9. That rules out 7.
  4. Row 2 (7 8 3 6) has one mark, already accounted for by 3. That rules out 8.
  5. Row 3 (4 2 9 8) has one mark still unexplained, and only one digit is left undecided: 4. So it is in the code.
  6. Row 1 (7 2 3 9) has one digit in the right spot. Since row 2 rules out the 3 in position 3, it has to be the 9 in position 4.
  7. The 3 has only one spot left: position 2 (row 5 rules out position 1, row 2 rules out position 3, and position 4 is already 9).
  8. The 4 has only one spot left: position 3 (row 3 rules out position 1, position 2 is already 3, and position 4 is already 9).
  9. That leaves the 5 for position 1.

That cracks it: the code is 5349.

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