Record of the numbers shown on the top face of a die, rolled 20 times, is shown below:
  1, 3, 5, 6, 6, 3, 5, 4, 1, 6, 2, 5, 1, 4, 6, 1, 6, 4, 1, 1
Which two numbers appear same number of times?

Answer

To solve the problem of finding which two numbers appear the same number of times when a die is rolled 20 times, we can follow these steps:

### Step-by-Step Solution:

1. **List the Numbers Rolled**:
We start with the numbers that were rolled:
1, 3, 5, 6, 6, 3, 5, 4, 1, 6, 2, 5, 1, 4, 6, 1, 6, 4, 1, 1.

2. **Count the Frequency of Each Number**:
We need to count how many times each number (from 1 to 6) appears in the list.
- Count for 1: 6 times
- Count for 2: 2 times
- Count for 3: 2 times
- Count for 4: 3 times
- Count for 5: 3 times
- Count for 6: 5 times

3. **Create a Frequency Table**:
We can organize this information into a table for clarity:

| Number | Frequency |
|--------|-----------|
| 1 | 6 |
| 2 | 2 |
| 3 | 2 |
| 4 | 3 |
| 5 | 3 |
| 6 | 5 |

4. **Identify Numbers with the Same Frequency**:
Now, we look for numbers that have the same frequency:
- The numbers 3 and 2 both appear 2 times.
- The numbers 4 and 5 both appear 3 times.

5. **Conclusion**:
The two numbers that appear the same number of times are:
- 3 and 2 (2 times)
- 4 and 5 (3 times)

### Final Answer:
The two numbers that appear the same number of times are **3 and 2** (2 times) and **4 and 5** (3 times).

---