In a certain coded languages:

A. 'Best way to win' is written as baumaushausa'

B. The way to hell' is written as "tau mausahau'

C. 'Win of the day' is written as 'shaufau tau dau'

What is the code for 'hell' in this language?

The correct answer is 'hau'.

To decode the language, we compare the three coded sentences by identifying words and their corresponding codes that appear in more than one sentence. Let us first lay out the sentences clearly:

A. 'Best way to win' → bau | mau | shau | sa
B. 'The way to hell' → tau | mau | sa | hau
C. 'Win of the day' → shau | fau | tau | dau

Step 1: Compare Sentences B and C

Look at sentences B and C side by side:

Sentence B: 'The way to hell' → tau | mau | sa | hau
Sentence C: 'Win of the day' → shau | fau | tau | dau

The word 'the' is common to both sentences B and C. The code 'tau' is the only code that appears in both coded strings. Therefore:

'the' = 'tau'

Step 2: Compare Sentences A and B

Look at sentences A and B side by side:

Sentence A: 'Best way to win' → bau | mau | shau | sa
Sentence B: 'The way to hell' → tau | mau | sa | hau

The words 'way' and 'to' are common to both sentences. The codes 'mau' and 'sa' appear in both coded strings. This confirms that:

{ 'mau', 'sa' } = { 'way', 'to' } (in some order)

Step 3: Isolate the code for 'hell'

Now focus on Sentence B: 'The way to hell' → tau | mau | sa | hau

- We already know 'tau' = 'the' (from Step 1).
- We already know 'mau' and 'sa' together account for 'way' and 'to' (from Step 2).

That leaves only one code and one word unaccounted for in Sentence B:

Remaining code: 'hau'
Remaining word: 'hell'

Therefore, by elimination:

'hell' = 'hau'

The code for 'hell' in this language is 'hau'.