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Kode #58: hints & solution

Here's the clue board for Kode #58. 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.

  • 17503▲1●1
  • 23907▲0●1
  • 34928▲0●2
  • 40862▲0●2
  • 51304▲0●0

Spoiler-free hints

  • 2 of the four digits are even.
  • The four digits add up to 22.
  • 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 (1 3 0 4) has no marks at all, so 1, 3, 0, and 4 are not in the code.
  2. Row 1 (7 5 0 3) has 2 marks still unexplained, and only 2 digits are left undecided: 7 and 5. So both are in the code.
  3. Row 2 (3 9 0 7) has one mark, already accounted for by 7. That rules out 9.
  4. Row 3 (4 9 2 8) has 2 marks still unexplained, and only 2 digits are left undecided: 2 and 8. So both are in the code.
  5. Row 4 (0 8 6 2) has 2 marks, already accounted for by 8 and 2. That rules out 6.
  6. Position 4 can only be 5 (row 4 rules out 2, row 2 rules out 7, and row 3 rules out 8).
  7. Row 1 (7 5 0 3) has one digit in the right spot. Since the 5 is already in position 4, it has to be the 7 in position 1.
  8. The 2 has only one spot left: position 2 (row 3 rules out position 3, position 1 is already 7, and position 4 is already 5).
  9. That leaves the 8 for position 3.

That cracks it: the code is 7285.

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