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Kode #51: hints & solution

Here's the clue board for Kode #51. 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.

  • 15429▲1●1
  • 26319▲0●2
  • 34968▲0●1
  • 48029▲0●0
  • 53968▲1●0

Spoiler-free hints

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

That cracks it: the code is 3451.

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