A die has six faces marked 0, 1, 1, 1, 6, 6. Two such dice are thrown together and total scores are recorded.
How many different scores are possible?

Answer

To find how many different scores are possible when two dice marked 0, 1, 1, 1, 6, 6 are thrown together, we can follow these steps:

### Step 1: Identify the possible outcomes for a single die.
The faces of the die are marked as follows:
- 0
- 1
- 1
- 1
- 6
- 6

From this, we can see that the possible outcomes when rolling one die are 0, 1, and 6.

### Step 2: List the possible outcomes when two dice are rolled.
When we roll two dice, we can combine the outcomes of each die. We will denote the outcomes of the first die as \(D_1\) and the second die as \(D_2\). The possible combinations are:

1. \(D_1 = 0\) and \(D_2 = 0\) → Total = 0 + 0 = 0
2. \(D_1 = 0\) and \(D_2 = 1\) → Total = 0 + 1 = 1
3. \(D_1 = 0\) and \(D_2 = 6\) → Total = 0 + 6 = 6
4. \(D_1 = 1\) and \(D_2 = 0\) → Total = 1 + 0 = 1
5. \(D_1 = 1\) and \(D_2 = 1\) → Total = 1 + 1 = 2
6. \(D_1 = 1\) and \(D_2 = 6\) → Total = 1 + 6 = 7
7. \(D_1 = 6\) and \(D_2 = 0\) → Total = 6 + 0 = 6
8. \(D_1 = 6\) and \(D_2 = 1\) → Total = 6 + 1 = 7
9. \(D_1 = 6\) and \(D_2 = 6\) → Total = 6 + 6 = 12

### Step 3: Summarize the unique scores.
Now we will summarize the unique scores obtained from the combinations above:
- From the combinations, the possible total scores are: 0, 1, 2, 6, 7, and 12.

### Step 4: Count the unique scores.
The unique scores we have are:
- 0
- 1
- 2
- 6
- 7
- 12

Thus, the total number of different scores possible is **6**.

### Final Answer:
The number of different scores possible when two such dice are thrown together is **6**.

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