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Kode #79: hints & solution

Here's the clue board for Kode #79. 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.

  • 16721▲1●1
  • 24621▲0●2
  • 31349▲0●2
  • 45420▲0●0
  • 55683▲0●3

Spoiler-free hints

  • 2 of the four digits are even.
  • The four digits add up to 18.
  • 2 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 (5 4 2 0) has no marks at all, so 5, 4, 2, and 0 are not in the code.
  2. Row 2 (4 6 2 1) has 2 marks still unexplained, and only 2 digits are left undecided: 6 and 1. So both are in the code.
  3. Row 1 (6 7 2 1) has 2 marks, already accounted for by 6 and 1. That rules out 7.
  4. Row 5 (5 6 8 3) has 2 marks still unexplained, and only 2 digits are left undecided: 8 and 3. So both are in the code.
  5. Row 3 (1 3 4 9) has 2 marks, already accounted for by 1 and 3. That rules out 9.
  6. Row 1 (6 7 2 1) has one digit in the right spot. Since row 2 rules out the 1 in position 4, it has to be the 6 in position 1.
  7. The 3 has only one spot left: position 3 (row 3 rules out position 2, row 5 rules out position 4, and position 1 is already 6).
  8. The 1 has only one spot left: position 2 (row 2 rules out position 4, position 1 is already 6, and position 3 is already 3).
  9. That leaves the 8 for position 4.

That cracks it: the code is 6138.

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