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04-14-2005, 02:36 PM
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#1 | ||
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lolzcat
Join Date: Oct 2000
Location: Annapolis, Md
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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? Last edited by QuikSand : 04-14-2005 at 02:56 PM. |
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04-14-2005, 02:47 PM
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#2 |
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Grizzled Veteran
Join Date: Jan 2005
Location: Appleton, WI
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Are we assuming all 3 darts have to score? Does this assumption even matter?
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04-14-2005, 02:50 PM
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#3 | |
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Pro Starter
Join Date: Oct 2000
Location: Fairfax, VA
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Quote:
I assume not all 3 have to score since then it would be simply 1. |
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04-14-2005, 02:52 PM
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#4 | |
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Grizzled Veteran
Join Date: Jan 2005
Location: Appleton, WI
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Quote:
The question sounded smarter in my head.  |
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04-14-2005, 02:53 PM
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#5 | |
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Pro Starter
Join Date: Oct 2000
Location: Fairfax, VA
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Quote:
Don't feel bad, at least you read the question. I misunderstood what he was looking for. hehe |
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04-14-2005, 02:57 PM
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#6 |
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Grizzled Veteran
Join Date: Jan 2005
Location: Appleton, WI
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I'm going with....163. - highlight to read.
Last edited by BrianD : 04-14-2005 at 03:01 PM. |
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04-14-2005, 03:00 PM
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#7 |
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Head Coach
Join Date: Oct 2000
Location: North Carolina
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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. |
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04-14-2005, 03:16 PM
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#8 |
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College Prospect
Join Date: Oct 2000
Location: Louisburg, KS
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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
__________________
TRA, the Royal Ape Last edited by TRO : 04-14-2005 at 03:20 PM. |
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04-14-2005, 03:17 PM
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#9 |
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Coordinator
Join Date: Oct 2000
Location: The Black Hole
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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?
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04-14-2005, 03:21 PM
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#10 | |
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College Prospect
Join Date: Oct 2000
Location: Louisburg, KS
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Quote:
Because QS said we need to score all 3 darts and start at 3
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TRA, the Royal Ape |
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04-14-2005, 03:29 PM
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Hokie, Hokie, Hokie, Hi
Join Date: Mar 2001
Location: Kennesaw, GA
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Quote:
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04-14-2005, 03:31 PM
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#12 |
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Head Coach
Join Date: Oct 2000
Location: North Carolina
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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.
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04-14-2005, 03:32 PM
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#13 | |
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Coordinator
Join Date: Oct 2000
Location: The Black Hole
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Quote:
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04-14-2005, 03:32 PM
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#14 |
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Hokie, Hokie, Hokie, Hi
Join Date: Mar 2001
Location: Kennesaw, GA
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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 Last edited by VPI97 : 04-14-2005 at 03:37 PM. |
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04-14-2005, 03:35 PM
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Head Coach
Join Date: Oct 2000
Location: North Carolina
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Quote:
Triple 15, 19, and 20. |
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04-14-2005, 03:38 PM
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College Starter
Join Date: Jun 2002
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Quote:
Quote:
Got it?
__________________
Ability is what you're capable of doing. Motivation determines what you do. Attitude determines how well you do it. - Lou Holtz |
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04-14-2005, 03:38 PM
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Hokie, Hokie, Hokie, Hi
Join Date: Mar 2001
Location: Kennesaw, GA
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Quote:
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04-14-2005, 03:43 PM
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#18 |
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College Prospect
Join Date: Oct 2000
Location: The Flatlands of America
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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 = ???
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Post Count: Eleventy Billion - so deal with it! Last edited by Scarecrow : 04-14-2005 at 03:49 PM. |
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04-14-2005, 03:49 PM
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#19 |
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College Prospect
Join Date: Oct 2000
Location: Louisburg, KS
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That's 143 crow, not 163.
__________________
TRA, the Royal Ape |
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04-14-2005, 03:50 PM
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#20 | |
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lolzcat
Join Date: Oct 2000
Location: Annapolis, Md
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Quote:
163 seems to be our winner. Well done, gang. |
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04-14-2005, 03:57 PM
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#21 | |
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Hokie, Hokie, Hokie, Hi
Join Date: Mar 2001
Location: Kennesaw, GA
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Quote:
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