Lowest score impossible to get with 3 darts.

On a regular dartboard, with 3 throws. What is the lowest possible score you can't hit. Disregard the rules that you have to throw out with a double.

I got the answer by trying, but I want to know if theres a elegant way of getting the right answer.

Well can you miss the dart board all together? If one were to throw 3 darts at a dart board and completely miss each time, then they would accumulate no score at all

Um, wouldn't that be "1"?

It's the lowest score, and you can't hit (to) it in three darts...



Maybe you mean highest possible score... hmm, I'm thinking 301 - 141 = 160. You start at 301, right?

reply to post by BcnDiamond


if a dart must hit the scoring section the answers 3, if it just has to hit the board, the answer is 0, so lowest score you can('t) hit would be 0 i guess.

[edit on 23/1/09 by pieman]

Good question, would be interesting to know.

172, i would guess.

Originally posted by pieman
reply to post by BcnDiamond

 

if a dart must hit the scoring section the answers 3, if it just has to hit the board, the answer is 0, so lowest score you can('t) hit would be 0 i guess.

[edit on 23/1/09 by pieman]

He means with 3 scoring darts what is the least you cannot score. Any combination of 3 scoring darts, what is the lowest you cannot get.

oh right, i get ya, triple 20 is the highest scoring slot so 180 is the highest score on three darts, that'll leave 121 if you're playing 301 and 321 if you're playing 501.


EDIT: hang on, nope, still don't think i get it. cannot get, what?!?

[edit on 23/1/09 by pieman]

reply to post by andy1033


301 - 3*20 - 3*20 - 9 = 172

So a triple 20, another triple 20, and a nine would give you 172, so that is a possible score with three darts...

LOL , what i mean is:
You start from zero, then throw three darts, which must hit.
What is then the lowest possible score you can't hit.

The answer will come to you, if you calculate a couple possibilities, but really im looking for a simple explanation or formula for the correct answer.

Originally posted by Ian McLean
reply to post by andy1033

 

301 - 3*20 - 3*20 - 9 = 172

So a triple 20, another triple 20, and a nine would give you 172, so that is a possible score with three darts...

You have misread the question. He is asking what is the lowest number you cannot score with 3 scoring darts.

I think it is 172, as you cannot get that with 3 darts. If you guys can find a lower number than good luck to anyone.

Originally posted by BcnDiamond
LOL , what i mean is:
You start from zero, then throw three darts, which must hit.
What is then the lowest possible score you can't hit.

The answer will come to you, if you calculate a couple possibilities, but really im looking for a simple explanation or formula for the correct answer.

So is there a number lower than 172 that you can get?

have you worked out the answer?

Originally posted by andy1033

Originally posted by BcnDiamond
LOL , what i mean is:
You start from zero, then throw three darts, which must hit.
What is then the lowest possible score you can't hit.

The answer will come to you, if you calculate a couple possibilities, but really im looking for a simple explanation or formula for the correct answer.

So is there a number lower than 172 that you can get?

have you worked out the answer?

Yes there is, but your talking about numbers here and certain possibilities there must be a formula or something to calculate the answer. Ill give you a few thoughts before giving the answer.

I think the answer is the sum of
dart 1 maximum score
dart 2 maximum score
dart 3 first impossible score to hit with one dart

(or in different order)

I dont think there is a formula for the first impossible score with one dart, you just have to go threw all the possibilities


[edit on 23-1-2009 by Just-Think]

Consider the points you could make, with three darts. You can get 0-5 points by missing the first two darts:

miss, miss, miss = 0
miss, miss, one = 1
miss, miss, two = 2
miss, miss, three = 3
miss, miss, four = 4
miss, miss, five = 5

Then, you can get 6-11 points by hitting two triple 1's, and another miss or 1-5:

triple 1, triple 1, miss = 6
triple 1, triple 1, one = 7
triple 1, triple 1, two = 8
triple 1, triple 1, three = 9
triple 1, triple 1, four = 10
triple 1, triple 1, five = 11

That pattern repeats: two triple 2's plus another dart give 12-17:

triple 2, triple 2, miss = 12
triple 2, triple 2, one = 13
triple 2, triple 2, two = 14
triple 2, triple 2, three = 15
triple 2, triple 2, four = 16
triple 2, triple 2, five = 17

Allowing all possible scores, all the way though two triple 20's:

triple 20, triple 20, miss = 120
triple 20, triple 20, one = 121
triple 20, triple 20, two = 122
triple 20, triple 20, three = 123
triple 20, triple 20, four = 124
triple 20, triple 20, five = 125
...
triple 20, triple 20, single 20 = 140

Then, you have to look at non-singles for the third dart:

triple 20, triple 20, 21 (triple 7) = 141
triple 20, triple 20, 22 (double 11) = 142
triple 20, triple 20, 23 is prime, however - so 143 can't be hit!

301 - 143 = 158

as the highest 'impossible' score. If that's what the question was.

Assuming you don't have to double in I'd guess it would be 181.

Edit: Rethinking that. Would it be 1? If you have to score on all 3 shots the only numbers you couldn't hit are 1 and 2. 1 being the lesser.

[edit on 23-1-2009 by intrepid]

You all need to disregard the start from 301 or 501.

Ian you gave some reason, and it didn't really matter you started from 301. But 143 is incorrect. It's actually the first number most people come up with. But 60+57+26 = 143.

You don't need to end with a double. Anything goes.

Originally posted by Ian McLean

301 - 143 = 158

as the highest 'impossible' score. If that's what the question was.

I think you are correct if you forget the last part, the answer is 143 in my opinion..

The lowest score would be "nothing" because right as the last dart hits... the power goes out. Unfortunately for you it was electronic darts.

Even if you miss it still scores as a 0... every dart you throw is scored, even if that score is 0. 0 is just the default score. which is where you start when the game begins.

[edit on 23-1-2009 by Wertdagf]

reply to post by Ian McLean


143 = (triple 19, bull, double 18)

166 or 172.

[edit on 1/23/2009 by andy1033]

Originally posted by andy1033
reply to post by Ian McLean

 

143 = 51(triple 19, bull, double 18)

166 or 172.

That would be correct if three times 19 would be 51 yes