In a certain code language, the expression 4 * 7 * 2 is evaluated as 361 and 5 * 9 * 1 is evaluated as 480. Using the same special operation rule on three numbers, what is the value of 2 * 1 * 3?

Introduction / Context:
This coding–decoding puzzle defines a special three-number operation using the symbol *. The numeric results look like three-digit codes rather than normal arithmetic. Our goal is to decode the pattern from the two worked examples and then apply it to 2, 1, and 3.

Given Data / Assumptions:

• 4 * 7 * 2 = 361.
• 5 * 9 * 1 = 480.
• The same rule must be used to find 2 * 1 * 3.
• All three numbers are single- or double-digit integers, and the answer is a three-digit number created by some pattern.

Concept / Approach:
Instead of doing usual arithmetic, we look at how each of the three numbers might correspond to each digit in the result. A useful strategy is to check whether each number is modified in a simple way, such as subtracting 1, and then written side by side to form the final code.

Step-by-Step Solution:
Step 1: Examine 4 * 7 * 2 = 361. If we subtract 1 from each number, we get: 4 - 1 = 3, 7 - 1 = 6, 2 - 1 = 1. Step 2: Concatenate these results: 3, 6, and 1 become 361, exactly matching the given code. Step 3: Check the second example 5 * 9 * 1 = 480. Subtract 1 from each number: 5 - 1 = 4, 9 - 1 = 8, 1 - 1 = 0. Step 4: Concatenate 4, 8, and 0 to get 480, confirming that the rule is consistent. Step 5: Apply the same rule to 2 * 1 * 3. Subtract 1 from each: 2 - 1 = 1, 1 - 1 = 0, 3 - 1 = 2. Step 6: Concatenate these digits: 1, 0, and 2 to obtain 102.

Verification / Alternative check:
We have verified this pattern on both given examples. Any alternative rule must also produce 361 from 4, 7, 2 and 480 from 5, 9, 1. The simple “subtract one from each and join the results” rule satisfies both cases neatly, so it is safe to apply it to 2, 1, and 3.

Why Other Options Are Wrong:
The other answer choices (312, 324, 210) correspond to other permutations or combinations of the numbers 1, 0, and 2 or to unrelated patterns, but they do not match the strict rule of “each number minus one in the original order.” Only 102 respects this rule exactly.

Common Pitfalls:
Students often try to add, multiply, or square the numbers, which quickly leads to inconsistent results. Another common confusion is to rearrange the digits or treat them as normal multiplication. Remember that this is a coding pattern, not standard arithmetic.

Final Answer:
Using the same coding rule, the value of 2 * 1 * 3 is 102.