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Kode #133: hints & solution

Here's the clue board for Kode #133. 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.

  • 12940▲1●1
  • 22745▲0●1
  • 37482▲0●2
  • 44318▲1●1
  • 54036▲0●0

Spoiler-free hints

  • 2 of the four digits are even.
  • The four digits add up to 20.
  • 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 5 (4 0 3 6) has no marks at all, so 4, 0, 3, and 6 are not in the code.
  2. Row 1 (2 9 4 0) has 2 marks still unexplained, and only 2 digits are left undecided: 2 and 9. So both are in the code.
  3. Row 2 (2 7 4 5) has one mark, already accounted for by 2. That rules out 7 and 5.
  4. Row 3 (7 4 8 2) has one mark still unexplained, and only one digit is left undecided: 8. So it is in the code.
  5. Row 4 (4 3 1 8) has one mark still unexplained, and only one digit is left undecided: 1. So it is in the code.
  6. Row 1 (2 9 4 0) has one digit in the right spot. Since row 2 rules out the 2 in position 1, it has to be the 9 in position 2.
  7. The 2 has only one spot left: position 3 (row 2 rules out position 1, row 3 rules out position 4, and position 2 is already 9).
  8. Row 4 (4 3 1 8) has one digit in the right spot. Since position 3 is already 2, it has to be the 8 in position 4.
  9. That leaves the 1 for position 1.

That cracks it: the code is 1928.

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