Decoding the Alphabetical Coding Logic for FLOWER, SHIFT, and VOLUME

This question involves a coding puzzle where words are assigned numerical codes. We need to decipher the underlying logic using the given examples, 'FLOWER' coded as '166' and 'SHIFT' coded as '73', and then apply it to find the code for 'VOLUME'.

Step 1: Analyzing the Pattern - Reverse Alphabetical Positions

Let's first examine the relationship between the letters of the words and their assigned codes. We'll consider the standard alphabetical positions (A=1, B=2, ..., Z=26) and the reverse positions (A=26, B=25, ..., Z=1).

The reverse position of a letter can be calculated using the formula: $ \text{Reverse Position} = 26 - (\text{Standard Position}) + 1 $.

Step 2: Calculating Reverse Position Sums

Let's calculate the sum of the reverse alphabetical positions for the letters in 'FLOWER' and 'SHIFT'.

FLOWER Calculation:

The word 'FLOWER' has 6 letters. The reverse positions are:

Sum of reverse positions for 'FLOWER' = $21 + 15 + 12 + 4 + 22 + 9 = 83$.

The given code for 'FLOWER' is 166. Notice that $ 83 \times 2 = 166 $.

SHIFT Calculation:

The word 'SHIFT' has 5 letters. The reverse positions are:

Sum of reverse positions for 'SHIFT' = $8 + 19 + 18 + 21 + 7 = 73$.

The given code for 'SHIFT' is 73. Notice that $ 73 \times 1 = 73 $.

Step 3: Identifying the Multiplier - Number of Vowels

From the calculations above, we see that the sum of reverse positions is multiplied by a factor:

• For 'FLOWER', the sum (83) was multiplied by 2 to get 166. 'FLOWER' has 2 vowels (O, E).
• For 'SHIFT', the sum (73) was multiplied by 1 to get 73. 'SHIFT' has 1 vowel (I).

This suggests the multiplier is equal to the number of vowels in the word.

Step 4: Applying the Logic to VOLUME

Now, let's apply this confirmed logic to the word 'VOLUME'.

The word 'VOLUME' has 6 letters.

First, find the sum of the reverse alphabetical positions:

Sum of reverse positions for 'VOLUME' = $5 + 12 + 15 + 6 + 14 + 22 = 74$.

Next, count the number of vowels in 'VOLUME'. The vowels are O, U, E. There are 3 vowels.

Finally, apply the rule: Multiply the sum of reverse positions by the number of vowels.

Code for 'VOLUME' = (Sum of reverse positions) $\times$ (Number of vowels)

Code for 'VOLUME' = $74 \times 3 = 222$.

Conclusion

Based on the derived coding logic (Sum of reverse alphabetical positions multiplied by the number of vowels), the code for 'VOLUME' is 222.