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Kode #197: hints & solution

Here's the clue board for Kode #197. Start with the spoiler-free hints. If you're still stuck, the full step-by-step solution is below, hidden until you open it.

Play Kode #197

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.

  • 13872▲1●1
  • 29542▲0●2
  • 33279▲0●1
  • 41620▲0●0
  • 51087▲0●2

Spoiler-free hints

  • 2 of the four digits are even.
  • The four digits add up to 24.
  • 3 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 (1 6 2 0) has no marks at all, so 1, 6, 2, and 0 are not in the code.
  2. Row 5 (1 0 8 7) has 2 marks still unexplained, and only 2 digits are left undecided: 8 and 7. So both are in the code.
  3. Row 1 (3 8 7 2) has 2 marks, already accounted for by 8 and 7. That rules out 3.
  4. Row 3 (3 2 7 9) has one mark, already accounted for by 7. That rules out 9.
  5. Row 2 (9 5 4 2) has 2 marks still unexplained, and only 2 digits are left undecided: 5 and 4. So both are in the code.
  6. Row 1 (3 8 7 2) has one digit in the right spot. Since row 3 rules out the 7 in position 3, it has to be the 8 in position 2.
  7. The 7 has only one spot left: position 1 (row 3 rules out position 3, row 5 rules out position 4, and position 2 is already 8).
  8. The 4 has only one spot left: position 4 (row 2 rules out position 3, position 1 is already 7, and position 2 is already 8).
  9. That leaves the 5 for position 3.

That cracks it: the code is 7854.

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