Kode #138: hints & solution
Here's the clue board for Kode #138. 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.
- 15468▲1●1
- 25421▲0●1
- 33258▲0●1
- 40375▲0●2
- 50851▲0●0
Spoiler-free hints
- 2 of the four digits are even.
- The four digits add up to 20.
- 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.
- Row 5 (0 8 5 1) has no marks at all, so 0, 8, 5, and 1 are not in the code.
- Row 1 (5 4 6 8) has 2 marks still unexplained, and only 2 digits are left undecided: 4 and 6. So both are in the code.
- Row 2 (5 4 2 1) has one mark, already accounted for by 4. That rules out 2.
- Row 3 (3 2 5 8) has one mark still unexplained, and only one digit is left undecided: 3. So it is in the code.
- Row 4 (0 3 7 5) has one mark still unexplained, and only one digit is left undecided: 7. So it is in the code.
- That makes all four digits of the code: 3, 4, 6, and 7. Every other digit is out, which also rules out 9.
- Row 1 (5 4 6 8) has one digit in the right spot. Since row 2 rules out the 4 in position 2, it has to be the 6 in position 3.
- The 3 has only one spot left: position 4 (row 3 rules out position 1, row 4 rules out position 2, and position 3 is already 6).
- The 4 has only one spot left: position 1 (row 2 rules out position 2, position 3 is already 6, and position 4 is already 3).
- That leaves the 7 for position 2.
That cracks it: the code is 4763.