Decoding the Code for 'Machine makes our life easy'

This question involves decoding a simple substitution code based on the positions or presence of words and digits in given phrases.

We are given two coded statements:

• 6218 means ‘Laptop is a computer’
• 8217 means ‘Computer is a machine’

Our goal is to find the code for the phrase ‘Machine makes our life easy’.

Step-by-Step Decoding Analysis

Let's compare the two given statements to identify common words and their corresponding codes.

Statement 1: ‘Laptop is a computer’ → 6218

Statement 2: ‘Computer is a machine’ → 8217

Comparing the words in both statements:

• Words common to both statements: ‘is’, ‘a’, ‘computer’
• Digits common to both codes: 8, 2, 1

This implies that the codes for ‘is’, ‘a’, and ‘computer’ are some permutation of the digits 8, 2, and 1. We cannot determine the exact code for each of these three words individually from these two statements alone.

Now let's look at the unique words and their potential codes:

• In Statement 1, the unique word is ‘Laptop’. The unique digit is 6. So, the code for ‘Laptop’ is likely 6.
• In Statement 2, the unique word is ‘machine’. The unique digit is 7. So, the code for ‘machine’ is likely 7.

So far, we have determined the following potential codes:

Finding the Code for 'Machine makes our life easy'

We need to find the code for ‘Machine makes our life easy’. From our analysis, we know the code for ‘Machine’ is 7.

The phrase is ‘Machine makes our life easy’. The words are ‘Machine’, ‘makes’, ‘our’, ‘life’, and ‘easy’.

We know the code for ‘Machine’ is 7.

The words ‘makes’, ‘our’, ‘life’, and ‘easy’ do not appear in the original coded phrases (‘Laptop is a computer’ and ‘Computer is a machine’).

This implies that the codes for these new words should be digits that were NOT used for the words in the original phrases.

The digits used in the original codes (6218 and 8217) are 1, 2, 6, 7, and 8.

Therefore, the codes for ‘makes’, ‘our’, ‘life’, and ‘easy’ must be chosen from digits NOT in the set $\{1, 2, 6, 7, 8\}$. Possible digits include $0, 3, 4, 5, 9, \text{etc.}$.

Now let's examine the given options for the code of ‘Machine makes our life easy’:

The code must contain 7 (for ‘Machine’), and the remaining digits must be from the set of digits NOT used in the original phrases (i.e., not from $\{1, 2, 6, 7, 8\}$).

Option 1: 75344

• Contains 7 (matches ‘Machine’).
• The other digits are 5, 3, 4.
• Are 5, 3, 4 in the set $\{1, 2, 6, 7, 8\}$? No.
• This option is consistent with our logic: 7 for ‘Machine’, and 5, 3, 4 for ‘makes’, ‘our’, ‘life’, ‘easy’ (with one digit repeated).

Option 2: 58795

• Contains 7 (matches ‘Machine’).
• The other digits are 5, 8, 9.
• Is 8 in the set $\{1, 2, 6, 7, 8\}$? Yes. 8 is used for ‘is’, ‘a’, or ‘computer’.
• The words ‘is’, ‘a’, ‘computer’ are NOT in the phrase ‘Machine makes our life easy’. Therefore, the digit 8 should not appear in its code. This option is incorrect.

Option 3: 76834

• Contains 7 (matches ‘Machine’).
• The other digits are 6, 8, 3, 4.
• Is 6 in the set $\{1, 2, 6, 7, 8\}$? Yes (for ‘Laptop’).
• Is 8 in the set $\{1, 2, 6, 7, 8\}$? Yes (for ‘is’, ‘a’, or ‘computer’).
• The words ‘Laptop’, ‘is’, ‘a’, ‘computer’ are NOT in the phrase ‘Machine makes our life easy’. Therefore, the digits 6 and 8 should not appear in its code. This option is incorrect.

Option 4: 75894

• Contains 7 (matches ‘Machine’).
• The other digits are 5, 8, 9, 4.
• Is 8 in the set $\{1, 2, 6, 7, 8\}$? Yes (for ‘is’, ‘a’, or ‘computer’).
• The words ‘is’, ‘a’, ‘computer’ are NOT in the phrase ‘Machine makes our life easy’. Therefore, the digit 8 should not appear in its code. This option is incorrect.

Based on this analysis, only Option 1 (75344) follows the pattern where the code for ‘Machine’ is present, and the codes for the new words (‘makes’, ‘our’, ‘life’, ‘easy’) are digits not used for any of the words in the original coded phrases.

Conclusion

The code for ‘Machine makes our life easy’ is 75344, where 7 represents ‘Machine’ and the digits 5, 3, and 4 represent the remaining words (‘makes’, ‘our’, ‘life’, ‘easy’) in some order.

Revision Table: Coding Decoding Logic

Additional Information: Types of Coding Decoding

Coding and decoding questions often involve different patterns. Understanding these patterns helps in solving such problems.

• Letter Coding: Letters are replaced by other letters based on a pattern (e.g., shifting positions, reversing order).
• Number Coding: Words or letters are assigned numerical codes. This can be based on alphabetical position, a specific rule, or as seen in this question, a direct substitution where each word maps to a number.
• Symbol Coding: Letters or words are replaced by symbols.
• Mixed Letter and Number Coding: A combination of letters and numbers is used to code words or messages.
• Phrase Coding: Entire phrases are given specific codes, and decoding is done by comparing common elements, similar to this problem.

In phrase coding like this question, the position of the digit might not necessarily correspond to the position of the word, but the set of digits used corresponds to the set of words in the phrase.