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Kode #98: hints & solution

Here's the clue board for Kode #98. 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.

  • 14312▲1●1
  • 25382▲0●1
  • 37260▲0●2
  • 45103▲0●2
  • 57152▲0●0

Spoiler-free hints

  • 3 of the four digits are even.
  • The four digits add up to 13.
  • 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 5 (7 1 5 2) has no marks at all, so 7, 1, 5, and 2 are not in the code.
  2. Row 1 (4 3 1 2) has 2 marks still unexplained, and only 2 digits are left undecided: 4 and 3. So both are in the code.
  3. Row 2 (5 3 8 2) has one mark, already accounted for by 3. That rules out 8.
  4. Row 3 (7 2 6 0) has 2 marks still unexplained, and only 2 digits are left undecided: 6 and 0. So both are in the code.
  5. That makes all four digits of the code: 0, 3, 4, and 6. Every other digit is out, which also rules out 9.
  6. Row 1 (4 3 1 2) has one digit in the right spot. Since row 2 rules out the 3 in position 2, it has to be the 4 in position 1.
  7. The 0 has only one spot left: position 2 (row 4 rules out position 3, row 3 rules out position 4, and position 1 is already 4).
  8. The 3 has only one spot left: position 3 (row 4 rules out position 4, position 1 is already 4, and position 2 is already 0).
  9. That leaves the 6 for position 4.

That cracks it: the code is 4036.

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