In a certain code language, 'PEPPER' is coded as 76 and 'CUCUMBER' is coded as 86. How will 'CAULIFLOWER' be coded in that language?
This question presents a word coding problem where words are coded into numerical values. We are given two examples: 'PEPPER' coded as 76 and 'CUCUMBER' coded as 86. Our task is to find the code for 'CAULIFLOWER' using the same pattern.
Let's examine the provided examples to understand the coding rule. A common method in such problems is to assign numerical values to letters based on their position in the English alphabet (A=1, B=2, ..., Z=26) and then perform some operation (like summing, multiplying, etc.).
Let's find the alphabetical position value for each letter in 'PEPPER':
Now, let's try summing these values:
$$ \text{Sum} = 16 + 5 + 16 + 16 + 5 + 18 $$ $$ \text{Sum} = 76 $$| Letter | Alphabetical Position |
|---|---|
| P | 16 |
| E | 5 |
| P | 16 |
| P | 16 |
| E | 5 |
| R | 18 |
| Total Sum | 76 |
The calculated sum is 76, which exactly matches the given code for 'PEPPER'.
Let's apply the same method to 'CUCUMBER':
Let's sum these values:
$$ \text{Sum} = 3 + 21 + 3 + 21 + 13 + 2 + 5 + 18 $$ $$ \text{Sum} = 86 $$| Letter | Alphabetical Position |
|---|---|
| C | 3 |
| U | 21 |
| C | 3 |
| U | 21 |
| M | 13 |
| B | 2 |
| E | 5 |
| R | 18 |
| Total Sum | 86 |
The calculated sum is 86, which matches the given code for 'CUCUMBER'.
Based on the analysis of both examples, it appears the coding pattern is simply the sum of the alphabetical positions of all the letters in the word.
Now we apply this established pattern to find the code for 'CAULIFLOWER'. Let's list the alphabetical position of each letter:
Next, we sum these values:
$$ \text{Sum} = 3 + 1 + 21 + 12 + 9 + 6 + 12 + 15 + 23 + 5 + 18 $$Let's add them step by step:
$$ \text{Sum} = 4 + 21 + 12 + 9 + 6 + 12 + 15 + 23 + 5 + 18 $$ $$ \text{Sum} = 25 + 12 + 9 + 6 + 12 + 15 + 23 + 5 + 18 $$ $$ \text{Sum} = 37 + 9 + 6 + 12 + 15 + 23 + 5 + 18 $$ $$ \text{Sum} = 46 + 6 + 12 + 15 + 23 + 5 + 18 $$ $$ \text{Sum} = 52 + 12 + 15 + 23 + 5 + 18 $$ $$ \text{Sum} = 64 + 15 + 23 + 5 + 18 $$ $$ \text{Sum} = 79 + 23 + 5 + 18 $$ $$ \text{Sum} = 102 + 5 + 18 $$ $$ \text{Sum} = 107 + 18 $$ $$ \text{Sum} = 125 $$| Letter | Alphabetical Position |
|---|---|
| C | 3 |
| A | 1 |
| U | 21 |
| L | 12 |
| I | 9 |
| F | 6 |
| L | 12 |
| O | 15 |
| W | 23 |
| E | 5 |
| R | 18 |
| Total Sum | 125 |
The sum of the alphabetical positions of the letters in 'CAULIFLOWER' is 125.
Following the pattern observed in the examples, the code for 'CAULIFLOWER' is 125.
| Word | Letter Values (Alphabetical Position) | Sum of Values | Given Code | Pattern Match |
|---|---|---|---|---|
| PEPPER | 16, 5, 16, 16, 5, 18 | 76 | 76 | Yes |
| CUCUMBER | 3, 21, 3, 21, 13, 2, 5, 18 | 86 | 86 | Yes |
| CAULIFLOWER | 3, 1, 21, 12, 9, 6, 12, 15, 23, 5, 18 | 125 | ? | Predicted: 125 |
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Solving these problems requires carefully analyzing the given examples to identify the specific rule being used.
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