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Kode #56: hints & solution

Here's the clue board for Kode #56. 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.

  • 12469▲1●1
  • 25269▲0●2
  • 37183▲0●2
  • 41340▲0●0
  • 59804▲0●1

Spoiler-free hints

  • 3 of the four digits are even.
  • The four digits add up to 23.
  • 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 3 4 0) has no marks at all, so 1, 3, 4, and 0 are not in the code.
  2. Row 3 (7 1 8 3) has 2 marks still unexplained, and only 2 digits are left undecided: 7 and 8. So both are in the code.
  3. Row 5 (9 8 0 4) has one mark, already accounted for by 8. That rules out 9.
  4. Row 1 (2 4 6 9) has 2 marks still unexplained, and only 2 digits are left undecided: 2 and 6. So both are in the code.
  5. Row 2 (5 2 6 9) has 2 marks, already accounted for by 2 and 6. That rules out 5.
  6. Row 1 (2 4 6 9) has one digit in the right spot. Since row 2 rules out the 6 in position 3, it has to be the 2 in position 1.
  7. The 8 has only one spot left: position 4 (row 5 rules out position 2, row 3 rules out position 3, and position 1 is already 2).
  8. The 6 has only one spot left: position 2 (row 2 rules out position 3, position 1 is already 2, and position 4 is already 8).
  9. That leaves the 7 for position 3.

That cracks it: the code is 2678.

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