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Kode #57: hints & solution

Here's the clue board for Kode #57. 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.

  • 10962▲1●1
  • 28465▲0●2
  • 32673▲0●2
  • 40278▲0●0
  • 53401▲1●0

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

That cracks it: the code is 3956.

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