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Kode #185: hints & solution

Here's the clue board for Kode #185. 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.

  • 18502▲1●1
  • 27392▲0●2
  • 32863▲0●1
  • 42610▲0●0
  • 58137▲2●0

Spoiler-free hints

  • Exactly one of the four digits is even.
  • The four digits add up to 29.
  • 4 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 4 (2 6 1 0) has no marks at all, so 2, 6, 1, and 0 are not in the code.
  2. Row 1 (8 5 0 2) has 2 marks still unexplained, and only 2 digits are left undecided: 8 and 5. So both are in the code.
  3. Row 3 (2 8 6 3) has one mark, already accounted for by 8. That rules out 3.
  4. Row 2 (7 3 9 2) has 2 marks still unexplained, and only 2 digits are left undecided: 7 and 9. So both are in the code.
  5. That makes all four digits of the code: 5, 7, 8, and 9. Every other digit is out, which also rules out 4.
  6. Row 5 (8 1 3 7) has 2 digits in the right spot, and the 8 in position 1 and the 7 in position 4 are its only digits in the code, so they're locked in.
  7. Row 1 (8 5 0 2) has only one digit in the right spot, already accounted for by the 8 in position 1. So the 5 isn't in position 2.
  8. The 5 has only one spot left: position 3 (row 1 rules out position 2, position 1 is already 8, and position 4 is already 7).
  9. That leaves the 9 for position 2.

That cracks it: the code is 8957.

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