To solve the problem, we need to identify the property of the given set (25, 36, 511) and then find which of the provided options shares the same property.
### Step-by-Step Solution:
1. **Identify the Property of the Given Set:**
- The first two numbers are 25 and 36.
- 25 is \(5^2\) (the square of 5).
- 36 is \(6^2\) (the square of 6).
- The third number is 511. We need to check if it can be derived from the first two numbers.
2. **Analyze the Relationship:**
- Let's break down the digits of the first two numbers:
- For 25: The digits are 2 and 5.
- For 36: The digits are 3 and 6.
- Now, let's sum the first digits (2 from 25 and 3 from 36):
- \(2 + 3 = 5\) (which is the first digit of 511).
- Next, sum the second digits (5 from 25 and 6 from 36):
- \(5 + 6 = 11\) (which is the second digit of 511).
3. **Verify the Property:**
- The property we have identified is that the first digit of the third number is the sum of the first digits of the first two numbers, and the second digit of the third number is the sum of the second digits of the first two numbers.
4. **Check the Options:**
- Now we will check each option to see if they follow the same property.
**Option 1: (61, 29, 810)**
- First digits: \(6 + 2 = 8\) (first digit of 810).
- Second digits: \(1 + 9 = 10\) (second digit of 810).
- This option follows the property.
**Option 2: (71, 20, 164)**
- First digits: \(7 + 2 = 9\) (should be the first digit of 164, which is 1).
- This option does not follow the property.
**Option 3: (84, 21, 510)**
- First digits: \(8 + 2 = 10\) (should be the first digit of 510, which is 5).
- This option does not follow the property.
**Option 4: (56, 34, 18)**
- First digits: \(5 + 3 = 8\) (should be the first digit of 18, which is 1).
- This option does not follow the property.
5. **Conclusion:**
- The only option that follows the same property as the given set (25, 36, 511) is **Option 1 (61, 29, 810)**.
