Odd One Out Analysis

The question asks us to identify the number that does not follow the same pattern as the others from the given list. The list contains the numbers \(\text{231}\), \(\text{123}\), \(\text{312}\), and \(\text{124}\). We need to find the rule that applies to most numbers and see which one breaks it.

Number Pattern Identification

Let's examine the digits that make up each number:

• Option 1: \(\text{231}\) - Contains the digits 1, 2, and 3.
• Option 2: \(\text{123}\) - Contains the digits 1, 2, and 3.
• Option 3: \(\text{312}\) - Contains the digits 1, 2, and 3.
• Option 4: \(\text{124}\) - Contains the digits 1, 2, and 4.

We can observe a clear pattern here. The first three numbers (\(\text{231}\), \(\text{123}\), \(\text{312}\)) are all formed using exactly the same set of digits: {1, 2, 3}. They are different arrangements (permutations) of these three digits.

However, the fourth number, \(\text{124}\), uses a different set of digits: {1, 2, 4}. It includes the digit 4 instead of the digit 3.

Another way to see this pattern is by looking at the sum of the digits:

• \(\text{231}\): \(2 + 3 + 1 = 6\)
• \(\text{123}\): \(1 + 2 + 3 = 6\)
• \(\text{312}\): \(3 + 1 + 2 = 6\)
• \(\text{124}\): \(1 + 2 + 4 = 7\)

This confirms that \(\text{124}\) is different because its digits sum to 7, while the digits of the other numbers sum to 6.

Conclusion

Based on the analysis of the digits used and their sum, the number \(\text{124}\) is the odd one out because it does not consist of the digits 1, 2, and 3 like the other options.