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Kode #42: hints & solution

Here's the clue board for Kode #42. 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.

  • 11275▲1●1
  • 21872▲0●2
  • 38413▲0●2
  • 44619▲0●0
  • 52369▲0●1

Spoiler-free hints

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

That cracks it: the code is 3785.

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