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.
100 million trials seem to verify 3/4 that Steven found.
ct=0; hit=0;
a=0;
for trial=1:100000000
b=360*rand; c=360*rand;
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
disp([hit ct hit/ct])
finds
hits trials fraction
74996141 100000000 0.74996141
verifying 3/4
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Posted by Charlie
on 2023-01-24 11:36:21 |
3 ducks as a simulation
