Hello everybody!  I haven't posted in a long time.  But anyways...
     I was working on this problem called 'The fighting fishes of Siam' by the late, great, Sam Loyd and it states that
there are two kinds of fishes, king fish and devil fish.  They inevitably attack each other on sight.  Three devil fish
counterbalance one king fish.  Four devil fish can kill a king fish in 3 minutes with each additional fish making the new group
proportionately quicker. So I did the following... 4*3 = 12, 5*x=12, so x=2.4 or 144 seconds for 5 fish.
But the solution in the back of the book says that each fish added to a group of x fish reduces the time taken by 1/x. So for five fish they say it will take 135 seconds. The time is reduced by 1/4.  This seems reasonable, but what if one devil fish killed a king fish in 3 minutes with each additional fish making the new group proportionately quicker?  Then two fish would take no time at all!  What about three fish then? What's going on?