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Kode #83: hints & solution

Here's the clue board for Kode #83. 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.

  • 11905▲1●1
  • 22765▲0●2
  • 30458▲0●2
  • 43920▲0●0
  • 56394▲0●0

Spoiler-free hints

  • Exactly one of the four digits is even.
  • The four digits add up to 21.
  • 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 (3 9 2 0) has no marks at all, so 3, 9, 2, and 0 are not in the code.
  2. Row 1 (1 9 0 5) has 2 marks still unexplained, and only 2 digits are left undecided: 1 and 5. So both are in the code.
  3. Row 5 (6 3 9 4) has no marks at all, so 6 and 4 are not in the code.
  4. Row 2 (2 7 6 5) has one mark still unexplained, and only one digit is left undecided: 7. So it is in the code.
  5. Row 3 (0 4 5 8) has one mark still unexplained, and only one digit is left undecided: 8. So it is in the code.
  6. Row 1 (1 9 0 5) has one digit in the right spot. Since row 2 rules out the 5 in position 4, it has to be the 1 in position 1.
  7. The 5 has only one spot left: position 2 (row 3 rules out position 3, row 2 rules out position 4, and position 1 is already 1).
  8. The 8 has only one spot left: position 3 (row 3 rules out position 4, position 1 is already 1, and position 2 is already 5).
  9. That leaves the 7 for position 4.

That cracks it: the code is 1587.

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