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Kode #28: hints & solution

Here's the clue board for Kode #28. 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.

  • 16591▲1●1
  • 20841▲0●2
  • 35418▲1●1
  • 43092▲1●1
  • 50682▲0●0

Spoiler-free hints

  • Exactly one of the four digits is even.
  • The four digits add up to 17.
  • 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 11 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 (0 6 8 2) has no marks at all, so 0, 6, 8, and 2 are not in the code.
  2. Row 2 (0 8 4 1) has 2 marks still unexplained, and only 2 digits are left undecided: 4 and 1. So both are in the code.
  3. Row 3 (5 4 1 8) has 2 marks, already accounted for by 4 and 1. That rules out 5.
  4. Row 1 (6 5 9 1) has one mark still unexplained, and only one digit is left undecided: 9. So it is in the code.
  5. Row 4 (3 0 9 2) has one mark still unexplained, and only one digit is left undecided: 3. So it is in the code.
  6. That makes all four digits of the code: 1, 3, 4, and 9. Every other digit is out, which also rules out 7.
  7. Row 1 (6 5 9 1) has one digit in the right spot. Since row 2 rules out the 1 in position 4, it has to be the 9 in position 3.
  8. Row 3 (5 4 1 8) has one digit in the right spot. Since position 3 is already 9, it has to be the 4 in position 2.
  9. Row 4 (3 0 9 2) has only one digit in the right spot, already accounted for by the 9 in position 3. So the 3 isn't in position 1.
  10. The 1 has only one spot left: position 1 (row 2 rules out position 4, position 2 is already 4, and position 3 is already 9).
  11. That leaves the 3 for position 4.

That cracks it: the code is 1493.

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