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Kode #72: hints & solution

Here's the clue board for Kode #72. 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.

  • 13408▲1●1
  • 21409▲0●1
  • 34385▲1●1
  • 42571▲0●2
  • 50693▲0●0

Spoiler-free hints

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

That cracks it: the code is 4728.

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