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Kode #87: hints & solution

Here's the clue board for Kode #87. 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.

  • 14671▲1●1
  • 27651▲0●2
  • 30526▲0●2
  • 42689▲0●0
  • 59412▲0●2

Spoiler-free hints

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

That cracks it: the code is 4105.

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