Decoding MACHINE to DANGER: Alphabet Coding Explained

This problem involves a simple substitution cipher where letters are replaced by numbers based on a specific rule. We need to figure out the rule used to code the word $MACHINE$ and then apply it to the word $DANGER$.

Analyzing the Code for MACHINE

The word $MACHINE$ has 7 letters. The provided code is $19-7-9-14-15-20-11$.

Let's find the standard alphabetical position for each letter in $MACHINE$:

• M is the 13th letter
• A is the 1st letter
• C is the 3rd letter
• H is the 8th letter
• I is the 9th letter
• N is the 14th letter
• E is the 5th letter

Now, let's compare these positions with the given coded numbers:

Determining the Coding Pattern

Let's look at the difference between the Given Code and the Alphabetical Position for each letter:

• M: $19 - 13 = 6$
• A: $7 - 1 = 6$
• C: $9 - 3 = 6$
• H: $14 - 8 = 6$
• I: $15 - 9 = 6$
• N: $20 - 14 = 6$
• E: $11 - 5 = 6$

The pattern is consistent: each letter's code is obtained by adding 6 to its alphabetical position. The formula is: Coded Number = Alphabetical Position + 6.

Coding the Word DANGER

Now, we apply this rule (position + 6) to the word $DANGER$:

• D: The 4th letter. Code = $4 + 6 = 10$
• A: The 1st letter. Code = $1 + 6 = 7$
• N: The 14th letter. Code = $14 + 6 = 20$
• G: The 7th letter. Code = $7 + 6 = 13$
• E: The 5th letter. Code = $5 + 6 = 11$
• R: The 18th letter. Code = $18 + 6 = 24$

Final Code for DANGER

Combining these numbers, the code for $DANGER$ is $10-7-20-13-11-24$.