First, I need to figure out how the points are assigned for each area of the target. The target has three concentric circles, and each area gives a different number of points. From the image, there are three targets: the first scores 14 points, the second scores 16 points, and the third is unknown.

Each target has two darts thrown at it. For the first target, labeled "14 Points," there are two darts: one hits the innermost circle, and one hits the middle ring. Similarly, for the second target, "16 Points," one dart hits the innermost circle and the other hits the outermost ring. The third target has one dart in the innermost circle and one in the middle ring, but the points are unknown.

I need to assign point values to each area. Let's denote the areas:

• Let A be the points for hitting the innermost circle.

• Let B be the points for hitting the middle ring.

• Let C be the points for hitting the outermost ring.

Since the points are for hitting the area, and darts can hit different areas, the total points for two darts would be the sum of the points for each dart's hit.

For the first attempt: 14 points. From the image, one dart hit the innermost circle (A) and one hit the middle ring (B). So, A + B = 14.

For the second attempt: 16 points. One dart hit the innermost circle (A) and one hit the outermost ring (C). So, A + C = 16.

Now, for the third attempt, the darts are: one in the innermost circle (A) and one in the middle ring (B), so it should be A + B again, which is 14 points, right?

But that seems too straightforward, and probably I'm missing something because the third target is shown with a question mark, implying it might not be the same as the first.

Let me look at the image again. In the third target, it has two darts: one in the innermost and one in the middle ring, just like the first one. But in the first, it's 14, so why would the third be different?

Perhaps the points are not just for the area hit, but there might be a multiplier or something. But the problem says "the number of points depends on which one of the three areas you hit," so it should be a fixed value per area.

Maybe I misread the hits. Let me describe the image carefully.

There are three targets side by side.

First target: labeled "14 Points." It has two darts. One dart is in the innermost circle (dark circle), and one is in the middle ring (light gray ring). The outermost ring is untouched.

Second target: labeled "16 Points." One dart in innermost (dark circle), and one in the outermost ring (dark gray ring). The middle ring is untouched.

Third target: "???" Unlabeled. One dart in innermost (dark circle), and one in middle ring (light gray ring). Outermost untouched.

So, for first: hits on A and B, sum 14.

Second: hits on A and C, sum 16.

Third: hits on A and B, same as first.

But then third should be 14. But why is it a question mark? Maybe there's a trick.

Perhaps the areas have different points, but for the same areas, it should be same points.

Unless the points depend on the attempt or something, but that doesn't make sense.

Another thought: maybe the darts can hit multiple areas or something, but no, each dart hits one area.

Perhaps the scoring is not just the sum, but there might be a bonus or something, but the problem doesn't say that.

Let me read the problem again: "If you hit the target board, you score points. The number of points depends on which one of the three areas you hit."

And "Diana throws two darts, three times at the target board." So each time, she throws two darts at one target.

For each throw (attempt), she gets points based on where the two darts hit.

In the first attempt, with two darts, she hit A and B, got 14.

Second attempt, hit A and C, got 16.

Third attempt, hit A and B, so should be 14.

But why is it unknown? Perhaps I need to find the individual point values.

I have two equations:

A + B = 14 (1)

A + C = 16 (2)

But I have three variables, so I need another equation.

From the third target, it's also A and B, but I don't have new information.

Unless for the third attempt, the hits are different, but from the image, it's the same as first.

Look at the third target: the darts are both in A and B, just like first.

But in the first, it's shown with arrows pointing to the hits, similarly for others.

Perhaps the point values are not integers, or something.

Maybe the areas have points, but for the same area, it's consistent.

I think I need to consider that the points might be different for the same area in different contexts, but that seems unlikely.

Another idea: perhaps the "points" for the attempt are not simply the sum of the two hits, but there might be a different scoring system.

For example, maybe it's the product or something, but that would be weird.

Let's see the points: 14 and 16, both even, so A, B, C could be integers.

From (1) A + B = 14

(2) A + C = 16

Subtract (1) from (2): (A+C) - (A+B) = 16-14 => C - B = 2, so C = B + 2.

For the third attempt, A + B = 14, same as first.

But why is it a question mark? Perhaps because we don't know A and B individually, but we know the sum.

The question is to find the points for the third attempt, which is A+B, which is 14.

But that seems too easy, and the problem is probably expecting a different answer.

Perhaps for the third attempt, the darts are not both hitting; but the image shows two darts.

Let's count the darts. In each target, there are two darts.

First target: two darts, one in A, one in B.

Second: one in A, one in C.

Third: one in A, one in B.

So third is identical to first in terms of hits.

Unless the point system has a penalty or something, but no.

Another thought: perhaps the areas are not all separate; or maybe the scoring depends on the combination.

For example, hitting A and B might have a special score, but the problem says points depend on which area you hit, implying per dart.

The text says: "the number of points depends on which one of the three areas you hit." So for each dart, based on where it hits, you get points, and for two darts, you sum them.

I think that's the standard interpretation.

Perhaps for the same areas, the points are the same, so third should be 14.

But let's see the image; in the third target, the dart in the middle ring might be in a different position, but it's the same area.

Perhaps I misidentified the areas.

Let me describe the colors.

In the image, the target has three areas:

• Innermost: dark circle

• Middle: light gray ring

• Outermost: dark gray ring

For first target: one dart in innermost (dark), one in middle (light gray)

Second: one in innermost (dark), one in outermost (dark gray)

Third: one in innermost (dark), one in middle (light gray)

Same as first.

So A + B = 14 for first and third.

A + C = 16 for second.

So for third, it should be 14.

But why is it a question mark? Maybe because we need to find the actual number, but it's given as 14 for first.

Perhaps the points are not fixed; or maybe for the third attempt, it's different because of the way the darts are thrown, but that doesn't make sense.

Another idea: perhaps the "points" for the attempt are the score for that particular throw, and it might include a bonus for hitting certain areas, but the problem doesn't say that.

Let's read the problem carefully: "Diana throws two darts, three times at the target board. On the first attempt she scores 14 points and on the second 16 points. How many points does she score on the third attempt?"

And the image shows the hits for each attempt.

For the third attempt, the hits are shown, but the points are not given.

But from the hits, it's the same as first, so it should be 14.

Unless for the first attempt, the 14 points include something else, but I think not.

Perhaps the darts can miss the board, but in the image, all darts are on the board.

In all cases, darts are on the board.

Maybe for the third attempt, one dart is in a different area, but from the image, it's not.

Let's look at the third target in the image. The arrow is pointing to one dart in innermost, and one in middle, same as first.

Perhaps the question is to find how many points, but since A and B are unknown, but we have A+B=14, so it's 14.

I think I'm overcomplicating.

Perhaps the points are not per area, but the areas have different names or something.

Another thought: maybe the "three areas" are not the rings, but something else, but the image shows concentric circles.

Perhaps the scoring is that the innermost is high points, but we need to find the values.

But with two equations and three variables, I can't find unique values, but for the third attempt, I don't need the values, just the sum for that combination.

For A and B combination, it's 14, for A and C, it's 16, so for A and B again, 14.

I think the answer should be 14.

But let's see if there's a trick with the third target.

In the image, for the third target, the dart in the middle ring is on the line or something? But the arrows show it's in the middle ring.

Similarly for others.

Perhaps for the first attempt, the 14 points are for that specific throw, and for third, it might be different, but why.

I recall that in some games, the score might depend on the order or something, but here it's not specified.

Another idea: perhaps the points are awarded based on the area, but for multiple darts in the same area, there might be a penalty, but in this case, no two darts in the same area; each dart is in a different area for each attempt.

In first attempt, one in A, one in B, different areas.

Second, one in A, one in C, different.

Third, one in A, one in B, different.

So no issue.

Perhaps the target has a bullseye, and the points are for the center, but here it's three areas.

I think I should consider that the point values are integers, and find possible values.

From A + B = 14

A + C = 16

C = B + 2, as I had.

B and C are points for middle and outer.

Typically, inner has more points, so A > B > C, but not necessarily, but let's assume.

A + B = 14, A + C = 16, so since C = B+2, and A + (B+2) = 16, but A+B=14, so 14 +2 =16, which is consistent, but doesn't give new info.

For example, if B=5, then A=9, C=7.

Or B=6, A=8, C=8, but if A=8, B=6, C=8, then C and A are both 8, but outer and inner same points? Possible but unusual.

Or B=4, A=10, C=6.

But for the third attempt, A+B=14 always.

So it must be 14.

Perhaps for the third attempt, the points are different because it's a different throw, but that doesn't make sense.

Another thought: maybe the "three times" means she throws two darts each time, but the score is for the pair, and for the third, we need to find based on the hits.

But we have the hits.

Perhaps the image for the third attempt is not the hits, but something else, but it shows darts with arrows.

I think I have to accept that it's 14.

But let's look back at the image; in the third target, is the dart in the middle ring or outermost? No, the arrow points to the light gray, which is middle.

Similarly, in first, it's light gray for the second dart.

In the second target, the second dart is in dark gray, outermost.

So no ambiguity.

Perhaps the points are not for the areas, but for the rings, and the rings have different points, but same as areas.

I think I should consider that the score might be the product or something, but that would be strange.

For example, if A and B give 14, A and C give 16, then for A and B, 14.

But if it were product, AB=14, AC=16, then for third, A*B=14.

But 14 and 16 are not common for products; 14 could be 27 or 72, 16 could be 44 or 28, etc., but for the third, it would be the same as first, so 14.

But the problem says "score points," and points are usually added, not multiplied.

For example, in darts, you add the scores.

So I think sum is correct.

Perhaps there is a misprint or something, but I doubt it.

Another idea: perhaps for the third attempt, the darts are at different positions, but in the image, it's shown, and it's the same as first.

Let's read the text: "Diana throws two darts, three times at the target board." So three separate throws, each at a target.

First target: 14 points, hits on A and B.

Second: 16 points, hits on A and C.

Third: hits on A and B, so 14 points.

I think the answer is 14.

But since it's a puzzle, maybe there's a trick.

Perhaps the "points" for the attempt include a base score or something, but no.

Or maybe the areas have names, but no.

Let's count the points: 14 and 16, difference of 2, and C - B =2, so outer is 2 points more than middle? But usually inner is higher, but here A+C=16, A+B=14, so C > B, meaning outer has more points than middle? That seems counterintuitive, but possible if the areas have different point values.

For example, if outer is worth more, but in standard darts, inner is higher, but here it could be different.

But for the third attempt, it's A and B, 14.

I think I should go with 14.

Perhaps for the third attempt, we need to find the score, but since it's the same as first, it's 14.

But the question is to box the answer.

So I think it's 14.

But let's see if the image has a different hit for the third.

Upon close inspection, in the third target, the dart in the middle ring might be closer to the center or something, but it's still the middle area.

The area is defined, not the exact position.

So I think it's fine.

Perhaps the target has a different scoring in different attempts, but that doesn't make sense.

I recall that in some puzzles, the score might be for the combination, like if you hit both, you get a bonus, but here no indication.

For example, if hitting A and B gives a special score, but in this case, for first and third, it's the same combination, so same score.

Similarly for A and C.

So no.

I think I have to conclude that the third attempt scores 14 points.

So the answer should be 14.