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Kode #4: hints & solution

Here's the clue board for Kode #4. 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.

  • 11490▲1●1
  • 21230▲0●1
  • 31795▲0●2
  • 46708▲0●0
  • 53740▲0●2

Spoiler-free hints

  • Exactly one of the four digits is even.
  • The four digits add up to 21.
  • 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 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 (6 7 0 8) has no marks at all, so 6, 7, 0, and 8 are not in the code.
  2. Row 5 (3 7 4 0) has 2 marks still unexplained, and only 2 digits are left undecided: 3 and 4. So both are in the code.
  3. Row 2 (1 2 3 0) has one mark, already accounted for by 3. That rules out 1 and 2.
  4. Row 1 (1 4 9 0) has one mark still unexplained, and only one digit is left undecided: 9. So it is in the code.
  5. Row 3 (1 7 9 5) has one mark still unexplained, and only one digit is left undecided: 5. So it is in the code.
  6. Row 1 (1 4 9 0) has one digit in the right spot. Since row 3 rules out the 9 in position 3, it has to be the 4 in position 2.
  7. The 3 has only one spot left: position 4 (row 5 rules out position 1, row 2 rules out position 3, and position 2 is already 4).
  8. The 9 has only one spot left: position 1 (row 3 rules out position 3, position 2 is already 4, and position 4 is already 3).
  9. That leaves the 5 for position 3.

That cracks it: the code is 9453.

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