Four darts are thrown at a dart board with four rings, each ring has a different value, If all four darts hit the board, how many different point totals are possible?

Depends on the score values of the rings.

If the rings are labeled 2,7,25,87 then there are more values available than if the rings were 5,10,15,20, because no combination of smaller scores equals a larger score.

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To determine the number of different point totals possible when four darts are thrown at a dart board with four rings, each with a different value, we can break down the problem step by step.

First, let's consider the number of unique combinations of hitting the dart board. Each dart has four possible areas it can hit (the four rings). Since there are four darts in total, the number of unique combinations is calculated by multiplying the number of options for each dart.

4 options (rings) × 4 options (rings) × 4 options (rings) × 4 options (rings) = 256 possible unique combinations.

Now, let's focus on the point totals. Since each ring has a different value, the point totals depend on which rings the darts hit. We can calculate the total number of different point totals by considering all possible combinations of values with the four darts.

To simplify the explanation, let's assume the rings have point values of 1, 2, 3, and 4.

Now, let's break down the combinations:

- For a point total of 1, we can hit the ring with value 1 four times.
- For a point total of 2, we can hit the ring with value 2 four times.
- For a point total of 3, we have three possible combinations: 1 + 1 + 1, 2 + 1, or 3.
- For a point total of 4, we have five possible combinations: 1 + 1 + 1 + 1, 2 + 1 + 1, 2 + 2, 3 + 1, or 4.
- Continuing this process, we can calculate the number of different point totals possible.

Summing up the possibilities for each point total:

1 (4 combinations) + 2 (4 combinations) + 3 (3 combinations) + 4 (5 combinations) + ... = the total number of different point totals

By calculating these combinations, we can find the number of different point totals possible when four darts are thrown at a dart board with four rings, each with a different value.