Brain Teasers
Game of Darts
If playing darts, what is the lowest possible score you CAN'T get with three darts on a standard dart board?
Answer
163Scoring combinations to achieve 0 thru 162 points:
all three darts miss --- 0 points
1st misses (0 points), 2nd misses (0 points), 3rd hits single 1 thru 20 (1 thru 20 points) --- 1 thru 20 points
1st misses (0 points), 2nd hits single 20 (20 points), 3rd hits single 1 thru 20 (0 thru 20 points) --- 21 thru 40 points
1st misses (0 points), 2nd hits double 20 (40 points), 3rd hits single 1 thru 20 (1 thru 20 points) --- 41 thru 60 points
1st misses (0 points), 2nd hits triple 20 (60 points), 3rd hits single 1 thru 20 (1 thru 20 points) --- 61 thru 80 points
1st hits double 20 (40 points), 2nd hits double 20 (40 points), 3rd hits single 1 thru 20 (1 thru 20 points) --- 81 thru 100 points
1st hits double 20 (40 points), 2nd hits triple 20 (60 points), 3rd hits single 1 thru 20 (1 thru 20 points) --- 101 thru 120 points
1st hits triple 20 (60 points), 2nd hits triple 20 (60 points), 3rd hits single 1 thru 20 (1 thru 20 points) --- 121 thru 140 points
1st hits triple 20 (60 points), 2nd hits triple 20 (60 points), 3rd hits triple 7 (21 points) --- 60 + 60 + 21 = 141 points
1st hits triple 20 (60 points), 2nd hits triple 20 (60 points), 3rd hits double 11 (22 points) --- 60 + 60 + 22 = 142 points
1st hits triple 20 (60 points), 2nd hits triple 19 (57 points), 3rd hits double 13 (26 points) --- 60 + 57 + 26 = 143 points
1st hits triple 20 (60 points), 2nd hits triple 18 (54 points), 3rd hits double 15 (30 points) --- 60 + 54 + 30 = 144 points
1st hits triple 20 (60 points), 2nd hits triple 17 (51 points), 3rd hits double 17 (34 points) --- 60 + 51 + 34 = 145 points
1st hits triple 20 (60 points), 2nd hits triple 16 (48 points), 3rd hits double 19 (38 points) --- 60 + 48 + 38 = 146 points
1st hits triple 20 (60 points), 2nd hits triple 16 (48 points), 3rd hits triple 13 (39 points) --- 60 + 48 + 39 = 147 points
1st hits triple 20 (60 points), 2nd hits triple 16 (48 points), 3rd hits double 20 (40 points) --- 60 + 48 + 40 = 148 points
1st hits triple 20 (60 points), 2nd hits triple 19 (57 points), 3rd hits double 16 (32 points) --- 60 + 57 + 32 = 149 points
1st hits triple 20 (60 points), 2nd hits triple 18 (54 points), 3rd hits double 18 (36 points) --- 60 + 54 + 36 = 150 points
1st hits triple 20 (60 points), 2nd hits triple 17 (51 points), 3rd hits double 20 (40 points) --- 60 + 51 + 40 = 151 points
1st hits triple 20 (60 points), 2nd hits triple 20 (60 points), 3rd hits double 16 (32 points) --- 60 + 60 + 32 = 152 points
1st hits triple 20 (60 points), 2nd hits triple 19 (57 points), 3rd hits double 18 (36 points) --- 60 + 57 + 36 = 153 points
1st hits triple 20 (60 points), 2nd hits triple 18 (54 points), 3rd hits double 20 (40 points) --- 60 + 54 + 40 = 154 points
1st hits triple 20 (60 points), 2nd hits triple 19 (57 points), 3rd hits double 19 (38 points) --- 60 + 57 + 38 = 155 points
1st hits triple 20 (60 points), 2nd hits triple 20 (60 points), 3rd hits double 18 (36 points) --- 60 + 60 + 36 = 156 points
1st hits triple 20 (60 points), 2nd hits triple 19 (57 points), 3rd hits double 20 (40 points) --- 60 + 57 + 40 = 157 points
1st hits triple 20 (60 points), 2nd hits triple 20 (60 points), 3rd hits double 19 (38 points) --- 60 + 60 + 38 = 158 points
1st hits triple 20 (60 points), 2nd hits triple 20 (60 points), 3rd hits triple 13 (39 points) --- 60 + 60 + 39 = 159 points
1st hits triple 20 (60 points), 2nd hits triple 20 (60 points), 3rd hits double 20 (40 points) --- 60 + 60 + 40 = 160 points
1st hits triple 20 (60 points), 2nd hits triple 17 (51 points), 3rd hits center bull's eye (50 points) --- 60 + 51 + 50 = 161 points
1st hits triple 20 (60 points), 2nd hits triple 20 (60 points), 3rd hits triple 14 (42 points) --- 60 + 60 + 42 = 162 points
163 points can not be achieved for the following reasons:
If two darts each hit a triple 20 for 60 points each, that produces 120 points, which requires another 43 points to reach 163. 43, being prime, can not be achieved with any single, double, or triple score.
If one dart hits triple 20 and another hits the center bull's eye, that achieves 110 points, leaving the need for an additional 53 points. 53 is prime, so can not be reached by any hit.
If two darts both hit the center bull's eye for 100 points, that still leaves a need for 63 points. 63 is not prime, but can not be reached, since it would require a triple 21 (there is no 21 on a dart board).
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Comments
you cannot score 0 on a dart board, unless you miss and then it isn't clased as a score. There fore the lowest number you can't get with three valid darts is one, because if each dart is valid then the minimum score possible is three. if the dart misses then it isnt valid.
OK I don't play darts, but if you throw one dart, get one, and miss with the other two darts do they let you take them again?
I submitted this puzzle for maths, not logic so as far as I can see, 0 can be "scored" 1 can be scored with 3 darts etc all the way up
I submitted this puzzle for maths, not logic so as far as I can see, 0 can be "scored" 1 can be scored with 3 darts etc all the way up
Having looked at the previous comments, I agree that one is the lowest score you can't hit with three valid darts. However, the teaser itself doesn't state with three VALID darts, so it is possible to hit 1. Also 143 is possible, if you start with treble 17 (51), which leaves 92, which is treble 20 (60). This leaves 32, which is double 16. We think that the lowest is 163. Any thoughts?
what about 159 ?
ooops, 20s + 20s + 13s
if you throw three darts at a board, and two miss, then you have only "used" one dart to make a score not three. it is impossible to score 1 with three darts, the two that missed don't really count, because in reality you could just drop them on the floor, and claim that you have used three darts. using a standard dart board only darts that land in a designated scoring segment count as valid darts. there is no such scoring segment that scores 0. for the darts to count they have to land in the segments. if you throw three dart and only one lands in a scoring segment, then you have only scored using one dart, not three.
if we use a standard dart board, then we've got to usie the standard triples, doubles and bullseye=25 specifications. given that, the lowest is 159.
the answer is 159
i'd peg 143 60 51 32 (T20 T17 D16)
i'd peg 143 60 51 32 (T20 T17 D16)
oops....its 163
Aug 24, 2002
I think the submitter lacks a basic knowledge of darts. Treble 20= 60, treble 17= 51, and double 16= 32. therefor 60+51+32= 143.
i kno nothing about darts...so this one was a lil outta my lg
What about negative 1? It's low and you can't score it.
um, what?????
to answer the annoying "3 darts" question - if you miss the board completely, then fine, that doesnt count... but if you hit the board, just not inside the numbered part (so, that little inch or so strip along the edge), its a valid throw resulting in 0
Now, as for what numbers you cannot get... consider 23 the last important number because that is the first prime number not on the board (therefore unattainable). 23 on top of 120 does make 143 the SEEMINGLY lowest number, assuming the other 2 are as high as possible. However, as has been noted repeatedly, there are other combinations because you CAN score higher than 23. So this opens up a world of possibilities... and restrictions, too, i think. I will work on it and come back though, not enough time now.
The list of numbers between 0 and 60 not possible on a dart board are as follows - 23, 25, 29, 31, 35, 37, 41, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59. Obviously the HIGHEST number unattainable would be 179 (obviously with 180 as the ceiling, as its the highest possible). Combinations of additions must be taken into account for other numbers, though. Again, ill be back when i have more time
hahaha. I had to reread that comment about 7 times cause it said i had curse words in there.... i finally realized i transposed a C and the O in account. anyways
I have googled the rules for darts and as far as I can see, if I am playing an opponent and they throw three darts that miss the board, then their score is zero? What else could you write down? They don't get to take the throws again! I don't get the objections.
Oct 27, 2011
Ok,Considering S[1-10],D[2-40],T[3-60],outRing25 and bEye50...the score will be between min4 and max 170.
With a program.... an impossible one is 163... not sure its the lowest.... any numbers ... just to test my program? ;)
With a program.... an impossible one is 163... not sure its the lowest.... any numbers ... just to test my program? ;)
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