Dartboard puzzle
 

On a standard dartboard, there are several ways to score points:

- numbered areas from 1-20, including rings to score double and triple
- a bullseye, worth 25 points, and a double bullseye worth 50 points

On a standard turn of throwing darts, you throw exactly three darts.

It's possible to throw three darts and score 180 points -- three triple 20s. But there is no way at all to score 179. I can hit two triple 20s and a triple 19 to score 177, but it's impossible to score 178.


What is the lowest number that is impossible to score using three darts and the scoring system described above?


edit -- all thee darts must score, and in an effort to make this into an actual puzzle, how about we stick with integers of 3 or higher, mmmmkay?

Are we assuming all 3 darts have to score? Does this assumption even matter?

I assume not all 3 have to score since then it would be simply 1.

The question sounded smarter in my head. :)

Don't feel bad, at least you read the question. I misunderstood what he was looking for. hehe

I'm going with....163. - highlight to read.

Let's see. Getting to 140 with no "impossible numbers" seems pretty easy. You can get every combo to 60 using three darts and no doubling or tripling. You can then add 40 to that by doubling two darts and get to 100. You can then add another 40 to that by having two darts in triple 20 and one in 20.

I don't know if that makes sense on the screen, but it does in my head. I am sure that the answer is above 140.

Edited for color:

As Albion pointed out, the number is above 140. We need the first number you can't double or triple to from 120. You can get 21 by 3*7 and 22 by 11*2. There is no way to score 23 on one dart.

Answer 143

I'm just dumb, but why wouldn't it just be 2? Throw three darts, score three 1s, no double or triple and you have 3 points. So the lowest would be 2?

Because QS said we need to score all 3 darts and start at 3 :)

That's what I first came up with, too...But T20 + T17 + D16 = 143

I can't get 163--based on Brian's guess above. And I think that I have gone through the others in my head--though I was not keeping notes and pretending to work at the same time, so I may have missed one.

Dude, maybe I'm more stupid than I think, but I just don't get this.

Everything from 1-60 is out due to combinations of three singles
61-80 is out due to combos of 2 singles + 1 double
81-100 is out due to combos of 2 singles + 1 triple (or two doubles + 1 singles if you will)
101-120 is out due to combos of (1 double + 1 triple) + 1 single
121-140 is out die to 2 triples + 1 single
From 141-160, I was able to come up with them all due to brute force combos revolving around 2 trips and a double.

Beyond that, the first one I couldn't brute force was: 163

Edit - Found my inital answer via three trips...edited to reflect new answer

Triple 15, 19, and 20.

Got it?

Jinx (see edit)

162 = T20 + T20 + T14
163 = [s]T20 + T17 + D16[/s] - oops hit the 20 key 1 too many times...
164 = T20 + T18 + BE
165 = T20 + T19 + T16
166 = ???

That's 143 crow, not 163.

163 seems to be our winner. Well done, gang.