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Posted 13 February 2008 - 04:32 PM
Alex had just hung a new dartboard on the wall and
was stepping back to admire his handiwork. Ian and
Jamie actually weren't too sure, and Davey hardly
looked up from where he sat at the bar.
Well it's kind of diff'rent, now, isn't it? allowed Jamie.
Yeh, it looks simple - no doubles or triples or anything
agreed Ian. And just multiples of 5, added Davey, who
became curious enough to walk over. There's a lot of
scores no one could make on that board ... so, what's
That's exactly the point, beamed Alex. Simplicity!
Usually you blokes don't like my propositions, cuz they're
a little bit beyond yer brains don't ya know. So I'm making
this one really easy to understand. Ian started twitching,
and Jamie shuffled his feet a bit. They'd heard pitches
from Alex before, and hearing that this one was simple
made them a bit edgy.
I'm thinking of a number, continued Alex, an easy one: 25.
You get two darts and all you have to do is score 25 points.
Look at the combinations that win for you. Even odds,
and I'll even take away the out of bounds. If you don't
hit a number, you throw another dart. Two darts that
score, and the score has to be 25. Who's ready for a
When the boys were silent, Alex stepped up the pitch.
All right, two to one odds your quid against my two. Like
taking candy from a baby, but you caught me in a good
mood tonight. Ian shook his head, Jamie sat down to
think it over, and Davey sauntered back to the bar.
After a moment, Davey hollered, make it 3 to 1 and
you're on. Ouch! cried Alex, if I weren't such a sport
I might not agree, but hey - we're friends, aren't we?
Let's see what ya got!
Assuming that Davey was no great shakes at aiming
the darts, with the only thing assured being that two
darts end up scoring points, did Davey make a good
bet? Or did Alex do his friends in, one more time?
The radii of the four circles are as shown: 1, 2, 3 and 4
in some units.
Vidi vici veni.
Posted 13 February 2008 - 05:12 PM
Edited by PolishNorbi, 13 February 2008 - 05:13 PM.
Posted 13 February 2008 - 06:00 PM
"After careful consideration, I want to remove the offer of 3 to 1 and propose a counter-offer of give me an extra dart and keep the same rules. Only two darts count (any two that equal 25 is a winning score). And misses don't count.
Posted 13 February 2008 - 06:25 PM
Spoiler for solution
Nope. My solution was flawed. PolishNorbi's approach was simpler. I was trying to avoid problems that could result from failing to consider the possibilities together, since order is unimportant. That's why I suggested only 10 possible outcomes, while there are 16 if you include order. Oh well.
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