3 ducks have landed in a circular pond. What is the probability there is a diameter such that the semicircle on one side contains all of them?
Repeat for 4 ducks.
Note: consider the ducks to be randomly chosen points in a circle.
(In reply to
3 duck soln by Steven Lord)
removed bug; Steven was right.
ct=0; hit=0;
for a=0
for b=0:.1:359.9
for c=0:.1:359.9
ct=ct+1;
set=sort([a b c ]);
aa=set(1);bb=set(2);cc=set(3);
diff=[bb-aa cc-bb aa-cc+360];
if max(diff)>180
hit=hit+1;
end
end
end
end
disp([hit ct hit/ct])
finds
0.749665354938272
close enough to 3/4.
Edited on January 24, 2023, 10:44 am
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Posted by Charlie
on 2023-01-24 09:58:55 |
numerical integration for 3 ducks
