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Kode #135: hints & solution

Here's the clue board for Kode #135. 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.

  • 12784▲1●1
  • 26014▲0●2
  • 38641▲1●1
  • 49173▲0●2
  • 53760▲0●0

Spoiler-free hints

  • 2 of the four digits are even.
  • The four digits add up to 16.
  • Just one digit is 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 11 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 5 (3 7 6 0) has no marks at all, so 3, 7, 6, and 0 are not in the code.
  2. Row 2 (6 0 1 4) has 2 marks still unexplained, and only 2 digits are left undecided: 1 and 4. So both are in the code.
  3. Row 3 (8 6 4 1) has 2 marks, already accounted for by 4 and 1. That rules out 8.
  4. Row 1 (2 7 8 4) has one mark still unexplained, and only one digit is left undecided: 2. So it is in the code.
  5. Row 4 (9 1 7 3) has one mark still unexplained, and only one digit is left undecided: 9. So it is in the code.
  6. That makes all four digits of the code: 1, 2, 4, and 9. Every other digit is out, which also rules out 5.
  7. Row 1 (2 7 8 4) has one digit in the right spot. Since row 2 rules out the 4 in position 4, it has to be the 2 in position 1.
  8. The 1 has only one spot left: position 4 (row 4 rules out position 2, row 2 rules out position 3, and position 1 is already 2).
  9. Row 3 (8 6 4 1) has only one digit in the right spot, already accounted for by the 1 in position 4. So the 4 isn't in position 3.
  10. The 4 has only one spot left: position 2 (row 3 rules out position 3, position 1 is already 2, and position 4 is already 1).
  11. That leaves the 9 for position 3.

That cracks it: the code is 2491.

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