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Kode #141: hints & solution

Here's the clue board for Kode #141. 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.

  • 16805▲1●1
  • 26175▲0●1
  • 31702▲1●1
  • 41953▲1●0
  • 57513▲0●0

Spoiler-free hints

  • 3 of the four digits are even.
  • The four digits add up to 17.
  • 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 11 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 (7 5 1 3) has no marks at all, so 7, 5, 1, and 3 are not in the code.
  2. Row 2 (6 1 7 5) has one mark still unexplained, and only one digit is left undecided: 6. So it is in the code.
  3. Row 3 (1 7 0 2) has 2 marks still unexplained, and only 2 digits are left undecided: 0 and 2. So both are in the code.
  4. Row 1 (6 8 0 5) has 2 marks, already accounted for by 6 and 0. That rules out 8.
  5. Row 4 (1 9 5 3) has one mark still unexplained, and only one digit is left undecided: 9. So it is in the code.
  6. That makes all four digits of the code: 0, 2, 6, and 9. Every other digit is out, which also rules out 4.
  7. Row 1 (6 8 0 5) has one digit in the right spot. Since row 2 rules out the 6 in position 1, it has to be the 0 in position 3.
  8. Row 3 (1 7 0 2) has only one digit in the right spot, already accounted for by the 0 in position 3. So the 2 isn't in position 4.
  9. Row 4 (1 9 5 3) has one digit in the right spot, and the 9 in position 2 is its only digit in the code, so it's locked in.
  10. The 2 has only one spot left: position 1 (row 3 rules out position 4, position 2 is already 9, and position 3 is already 0).
  11. That leaves the 6 for position 4.

That cracks it: the code is 2906.

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