Step-by-step Solution:

Quick Solution

This puzzle involves a specific rule for converting letters into numbers based on their position in the alphabet. First, we need to deduce this rule from the given example, and then apply it to the new word.

1. Find the Encoding Rule from the Example

The example given is EXAMINATION → 56149512965.

The rule is to take the alphabetical position of each letter. If the position is a single digit (1-9), that digit is used. If the position is a two-digit number (10-26), its digits are summed up to get the code.

• E is the 5th letter → Code is 5.
• X is the 24th letter → Code is 2 + 4 = 6.
• A is the 1st letter → Code is 1.
• M is the 13th letter → Code is 1 + 3 = 4.
• ...and so on for the rest of the word.

2. Apply the Rule to GOVERNMENT

Now we apply the same "sum of digits" rule to each letter of the word "GOVERNMENT":

• G (is the 7th letter) → 7
• O (is the 15th letter) → 1 + 5 = 6
• V (is the 22nd letter) → 2 + 2 = 4
• E (is the 5th letter) → 5
• R (is the 18th letter) → 1 + 8 = 9
• N (is the 14th letter) → 1 + 4 = 5
• M (is the 13th letter) → 1 + 3 = 4
• E (is the 5th letter) → 5
• N (is the 14th letter) → 1 + 4 = 5
• T (is the 20th letter) → 2 + 0 = 2

3. Final Code

Assembling the digits in order gives us the final code.

Final Answer: The word 'GOVERNMENT' can be coded as 7645954552.