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Kode #55: hints & solution

Here's the clue board for Kode #55. 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.

  • 15124▲1●1
  • 29724▲0●1
  • 34896▲0●2
  • 43406▲0●2
  • 53196▲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 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 (3 1 9 6) has no marks at all, so 3, 1, 9, and 6 are not in the code.
  2. Row 3 (4 8 9 6) has 2 marks still unexplained, and only 2 digits are left undecided: 4 and 8. So both are in the code.
  3. Row 2 (9 7 2 4) has one mark, already accounted for by 4. That rules out 7 and 2.
  4. Row 1 (5 1 2 4) has one mark still unexplained, and only one digit is left undecided: 5. So it is in the code.
  5. Row 4 (3 4 0 6) has one mark still unexplained, and only one digit is left undecided: 0. So it is in the code.
  6. Row 1 (5 1 2 4) has one digit in the right spot. Since row 2 rules out the 4 in position 4, it has to be the 5 in position 1.
  7. The 4 has only one spot left: position 3 (row 4 rules out position 2, row 2 rules out position 4, and position 1 is already 5).
  8. The 8 has only one spot left: position 4 (row 3 rules out position 2, position 1 is already 5, and position 3 is already 4).
  9. That leaves the 0 for position 2.

That cracks it: the code is 5048.

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