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Kode #107: hints & solution

Here's the clue board for Kode #107. 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.

  • 15387▲1●1
  • 20382▲0●1
  • 35986▲0●2
  • 47296▲0●3
  • 54185▲0●0

Spoiler-free hints

  • Exactly one of the four digits is even.
  • The four digits add up to 25.
  • 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 8 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 (4 1 8 5) has no marks at all, so 4, 1, 8, and 5 are not in the code.
  2. Row 1 (5 3 8 7) has 2 marks still unexplained, and only 2 digits are left undecided: 3 and 7. So both are in the code.
  3. Row 2 (0 3 8 2) has one mark, already accounted for by 3. That rules out 0 and 2.
  4. Row 3 (5 9 8 6) has 2 marks still unexplained, and only 2 digits are left undecided: 9 and 6. So both are in the code.
  5. Row 1 (5 3 8 7) has one digit in the right spot. Since row 2 rules out the 3 in position 2, it has to be the 7 in position 4.
  6. The 9 has only one spot left: position 1 (row 3 rules out position 2, row 4 rules out position 3, and position 4 is already 7).
  7. The 3 has only one spot left: position 3 (row 2 rules out position 2, position 1 is already 9, and position 4 is already 7).
  8. That leaves the 6 for position 2.

That cracks it: the code is 9637.

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