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Kode #38: hints & solution

Here's the clue board for Kode #38. 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.

  • 17361▲1●1
  • 20561▲0●1
  • 34823▲0●1
  • 41579▲1●2
  • 54523▲0●0

Spoiler-free hints

  • Exactly one of the four digits is even.
  • The four digits add up to 25.
  • 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 5 (4 5 2 3) has no marks at all, so 4, 5, 2, and 3 are not in the code.
  2. Row 3 (4 8 2 3) has one mark still unexplained, and only one digit is left undecided: 8. So it is in the code.
  3. Row 4 (1 5 7 9) has 3 marks still unexplained, and only 3 digits are left undecided: 1, 7, and 9. So all of them are in the code.
  4. Row 1 (7 3 6 1) has 2 marks, already accounted for by 7 and 1. That rules out 6.
  5. Row 2 (0 5 6 1) has one mark, already accounted for by 1. That rules out 0.
  6. Row 1 (7 3 6 1) has one digit in the right spot. Since row 2 rules out the 1 in position 4, it has to be the 7 in position 1.
  7. Row 4 (1 5 7 9) has one digit in the right spot. Since position 1 is already 7 and the 7 is already in position 1, it has to be the 9 in position 4.
  8. The 8 has only one spot left: position 3 (row 3 rules out position 2, position 1 is already 7, and position 4 is already 9).
  9. That leaves the 1 for position 2.

That cracks it: the code is 7189.

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