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bonanova

Question

It was quiet at Morty's last night. But only for a few

minutes; then Alex walked in, with his usual enigmatic

smile. So I'm not so good with a target pistol as I am

at darts, he said, to no one in particular. But I am

pretty good a puzzles, if I do say.

That caught Davey's ear, and Jamie's too, as they

found their way to the table where Alex was looking at

the target he'd used the night before at the shooting

range.

Ya see the holes here, he said. Aidan and Ian and

myself here, we all had six shots. And even though

we had had a few cold ones before shooting, we kept

track of our separate shots long enough to know that

we all got exactly the same total score!

Now the question that I have for you geniuses is this.

Ya see here that only one shot hit the bullseye for 50

points. Beyond the fact all three of us had the same

total score, I'll tell you that Aidan scored 22 points on

his first two shots. And - quite amazingly, given my

level of skill at the thing - my first shot scored only 3.

Now if the two of you are as smart as ya make out

to be, one of you should be able to tell me who it was

that hit the bull. The bet is drinks for a week. Any

takers?

Davey and Jamie looked at the holes in the target and

noted the scores of each shot:

50 - 1

25 - 2

20 - 3

10 - 3

05 - 2

03 - 2

02 - 2

01 - 3

Davey stroked his beard and thought, while Jamie's

head began to spin. Finally Davey decided to take

the bet.

Should he have taken the bet?

Who hit the bull?

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Alex hit the bullseye.

There are 213 points scored in total, which is 71 points each.

If Aidan already has 22 points, then a bullseye would give him 72 points, so Aidan is right out.

The only way to score 71 points with six hits and one bullseye is by scoring 50, 10, 5, 3, 2, 1.

Given that Alex already has used one of the 3 point targets, he must also have a 2 in order to sum to 5 to total 70, plus each of them got a 1 for 71.

Given that Aidan already has used one of the 2 point targets, he must have a 3 to sum to 5 for the same reason as the above point.

There are no more 3's or 2's, so Ian could not have hit any, thus making it impossible for him to have hit the bullseye since there is only one combination of hits that can yield 71 including a bullseye.

These are the target hits, not necessarily in this order (pardon if the spacing is bad)

Aidan .... Ian .... Alex

. 20 ....... 25 ...... 3

.. 2 ........ 20 ..... 50

. 25 ....... 10 ..... 10

. 20 ....... 10 ...... 5

.. 3 ......... 5 ....... 2

.. 1 ......... 1 ....... 1

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With the amount of darts of each number given, we can see the total points is 213, so they all had 71 points on 6 shots. Using the information that Aidan scored 22 on his first 2 shots, there is only one combination of darts that accomplishes that (20+2). Then, he needs to score a 49 on his remaining 4 shots. I'm fairly certain that using the numbers given, there are only 2 possible combinations:

(25, 20, 3, 1) and (25, 20, 2, 2)

However, one of the two 2 darts was already taken in his first 2 shots, so he must have shot the following numbers (not particularly in order): 20, 2, 25, 20, 3, 1

This leaves the following numbers:

50 - 1

25 - 1

20 - 1

10 - 3

05 - 2

03 - 1

02 - 1

01 - 2

We know Alex's first shot was a 3, so that removes the 3's, and we need to find a total of 71 in 6 shots and a total of 68 in 5 shots. Trying to find out who scored the bull, I checked if it was possible for the 71 in 6 shots to include the 50 (if 21 in 5 shots is possible), and I believe it is not without either of the two 3's already taken by Aidan and Alex. Therefore, Alex scored the bull, and I believe these are the only possible combinations:

Aidan: 20, 2, 25, 20, 3, 1

Ian: 25, 20, 10, 10, 5, 1

Alex: 3, 50, 10, 5, 2, 1

So Alex (the speaker) scored the bull, and he did the right thing by taking the bet, since there was only one possible combination of darts to satisfy the requirements!

EDIT: gah, I took too long to type it all out, good job ChuckJerry, assuming we're right that is ;)

Edited by frotorious

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I'll not only tell you the answer, I'll tell you what shots everyone got.

The score everyone got here was 71. Add up all the points on the target, divide by 3.

Aiden couln't have been it, because he already had 22 points. Adding 50 to that gives 72, which is too high. The only way to get 71 starting with 22 points in two shots is this:

25, 20, 20, 3, 2, 1

We have 1x50, 1x25, 1x20, 2x5, 3x10, 1x2, and 2x1 remaining.

Say Ian got the 50. In five shots, he would have to get 21 points. There is no way to do this with the remaining shots, so it had to be Alex to get the bullseye.

So we now know that Alex had 53 points in two shots, which means he needed another 18 points in four shots. This comes out to:

50, 10, 5, 3, 2, 1

And we have Ian left with:

25, 20, 10, 10, 5, 1

In short, Alex got the bullseye.

EDIT: Well, I think the three of us must be right... we seem to all have gotten the same answer independently.

Edited by Seventh Sage

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