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Kode #3: hints & solution

Here's the clue board for Kode #3. 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.

  • 16490▲1●1
  • 26398▲0●1
  • 31904▲1●1
  • 46751▲0●3
  • 54827▲0●0

Spoiler-free hints

  • 2 of the four digits are even.
  • The four digits add up to 12.
  • 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 8 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 (4 8 2 7) has no marks at all, so 4, 8, 2, and 7 are not in the code.
  2. Row 4 (6 7 5 1) has 3 marks still unexplained, and only 3 digits are left undecided: 6, 5, and 1. So all of them are in the code.
  3. Row 2 (6 3 9 8) has one mark, already accounted for by 6. That rules out 3 and 9.
  4. Row 1 (6 4 9 0) has one mark still unexplained, and only one digit is left undecided: 0. So it is in the code.
  5. Row 1 (6 4 9 0) has one digit in the right spot. Since row 2 rules out the 6 in position 1, it has to be the 0 in position 4.
  6. Row 3 (1 9 0 4) has one digit in the right spot. Since the 0 is already in position 4, it has to be the 1 in position 1.
  7. The 5 has only one spot left: position 2 (row 4 rules out position 3, position 1 is already 1, and position 4 is already 0).
  8. That leaves the 6 for position 3.

That cracks it: the code is 1560.

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