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Kode #41: hints & solution

Here's the clue board for Kode #41. 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.

  • 19546▲1●1
  • 28521▲0●2
  • 35731▲0●2
  • 43876▲1●1
  • 59478▲0●0

Spoiler-free hints

  • 2 of the four digits are even.
  • The four digits add up to 16.
  • 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 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 (9 4 7 8) has no marks at all, so 9, 4, 7, and 8 are not in the code.
  2. Row 1 (9 5 4 6) has 2 marks still unexplained, and only 2 digits are left undecided: 5 and 6. So both are in the code.
  3. Row 4 (3 8 7 6) has one mark still unexplained, and only one digit is left undecided: 3. So it is in the code.
  4. Row 3 (5 7 3 1) has 2 marks, already accounted for by 5 and 3. That rules out 1.
  5. Row 2 (8 5 2 1) has one mark still unexplained, and only one digit is left undecided: 2. So it is in the code.
  6. That makes all four digits of the code: 2, 3, 5, and 6. Every other digit is out, which also rules out 0.
  7. Row 1 (9 5 4 6) has one digit in the right spot. Since row 2 rules out the 5 in position 2, it has to be the 6 in position 4.
  8. Row 4 (3 8 7 6) has only one digit in the right spot, already accounted for by the 6 in position 4. So the 3 isn't in position 1.
  9. The 3 has only one spot left: position 2 (row 4 rules out position 1, row 3 rules out position 3, and position 4 is already 6).
  10. The 2 has only one spot left: position 1 (row 2 rules out position 3, position 2 is already 3, and position 4 is already 6).
  11. That leaves the 5 for position 3.

That cracks it: the code is 2356.

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