The puzzle[]
- R1. Every button should be pushed once and only once.
- R2. Don't start by pushing '1'.
- R3. The letters should be pushed in the alphabetical order.
- R4. Push 'B' after two numbers have been pushed.
- R5. '3' should be pushed immediately after '1'.
- R6. Half the letters are immediately followed by a number.
- R7. Neither '3' nor '4' is the last number to be pushed
- R8. The final letter should be pushed immediately after all the numbers have been pushed.
The solution:[]
- D1. The letters are pushed in order, so 'A' is the first letter to be pushed and 'D' is the last (rule 3)
- D2. '13' can be considered one unit (rule 5)
- D3. '3' and '4' are not the last number buttons, '1' is before '3', so '2' must be the last number button to be pushed (rules 7 & 5)
- D4. Therefore '2D' is the ending sequence (rules 8 & 3)
- D5. There should be exactly two numbers before 'B' (rule 4), and '1' and '3' are a unit (D2), and '2' is the last number (deducted above), so '4' can't happen before 'B'. Because it would either cause in one or three numbers before 'B'. Therefore, '13' should happen before 'B'. They cannot happen before 'A' (rule 2), so the starting sequence is 'A13B'.
Now the only thing left is to decide the order of 'C' and 4'. Rule 6 says half of the letters (two letters) should be immediately followed by a number. The two possible sequences are:
A13B4C2D <- Contradicts rule 6 (Three letters A, B and C are followed by a number)
A13BC42D <- Correct combination.
Notes[]
From the Combo.text document in the FM ZIP file.