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Kode #74: hints & solution

Here's the clue board for Kode #74. 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.

  • 16284▲1●1
  • 26724▲0●2
  • 39580▲1●1
  • 47692▲1●1
  • 52104▲0●0

Spoiler-free hints

  • 2 of the four digits are even.
  • The four digits add up to 26.
  • 4 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 12 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 (2 1 0 4) has no marks at all, so 2, 1, 0, and 4 are not in the code.
  2. Row 1 (6 2 8 4) has 2 marks still unexplained, and only 2 digits are left undecided: 6 and 8. So both are in the code.
  3. Row 2 (6 7 2 4) has one mark still unexplained, and only one digit is left undecided: 7. So it is in the code.
  4. Row 4 (7 6 9 2) has 2 marks, already accounted for by 7 and 6. That rules out 9.
  5. Row 3 (9 5 8 0) has one mark still unexplained, and only one digit is left undecided: 5. So it is in the code.
  6. That makes all four digits of the code: 5, 6, 7, and 8. Every other digit is out, which also rules out 3.
  7. Row 1 (6 2 8 4) has one digit in the right spot. Since row 2 rules out the 6 in position 1, it has to be the 8 in position 3.
  8. Row 3 (9 5 8 0) has only one digit in the right spot, already accounted for by the 8 in position 3. So the 5 isn't in position 2.
  9. Position 2 can only be 6 (row 3 rules out 5 and row 2 rules out 7).
  10. Row 4 (7 6 9 2) has only one digit in the right spot, already accounted for by the 6 in position 2. So the 7 isn't in position 1.
  11. The 7 has only one spot left: position 4 (row 4 rules out position 1, position 2 is already 6, and position 3 is already 8).
  12. That leaves the 5 for position 1.

That cracks it: the code is 5687.

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