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Kode #81: hints & solution

Here's the clue board for Kode #81. 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.

  • 14326▲1●1
  • 20816▲0●2
  • 36825▲0●2
  • 45794▲0●0
  • 58207▲0●3

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

That cracks it: the code is 2380.

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