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Kode #63: hints & solution

Here's the clue board for Kode #63. 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.

  • 19514▲1●1
  • 27516▲0●1
  • 31682▲0●2
  • 44753▲0●0
  • 58103▲1●2

Spoiler-free hints

  • 2 of the four digits are even.
  • The four digits add up to 18.
  • 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 10 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 (4 7 5 3) has no marks at all, so 4, 7, 5, and 3 are not in the code.
  2. Row 1 (9 5 1 4) has 2 marks still unexplained, and only 2 digits are left undecided: 9 and 1. So both are in the code.
  3. Row 2 (7 5 1 6) has one mark, already accounted for by 1. That rules out 6.
  4. Row 5 (8 1 0 3) has 2 marks still unexplained, and only 2 digits are left undecided: 8 and 0. So both are in the code.
  5. Row 3 (1 6 8 2) has 2 marks, already accounted for by 1 and 8. That rules out 2.
  6. Row 1 (9 5 1 4) has one digit in the right spot. Since row 2 rules out the 1 in position 3, it has to be the 9 in position 1.
  7. Position 3 can only be 0 (row 2 rules out 1 and row 3 rules out 8).
  8. Row 5 (8 1 0 3) has only one digit in the right spot, already accounted for by the 0 in position 3. So the 1 isn't in position 2.
  9. The 1 has only one spot left: position 4 (row 5 rules out position 2, position 1 is already 9, and position 3 is already 0).
  10. That leaves the 8 for position 2.

That cracks it: the code is 9801.

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