A CARROLL,LEWIS PILLOW PROBLEM - PROBABILITY OF AN OBTUSE TRIANGLE

On the 100th anniversary (1993) of Lewis Carroll's Pillow Problems, Eu gene Seneta presented a selection of the problems the author, Charles Dodgson, claims to have solved while in bed. The selection omits the o ne problem in continuous probability: ''Three points are taken at rand om on an infinite plane. Find the chance of their being the vertices o f an obtuse-angled triangle.'' Charles Dodgson presents a solution tha t involves a clear error in conditioning. An alternative solution is s uggested here. This solution seems rather natural and should be especi ally appealing to statisticians. The nature of the solution suggests a method for using transformation groups to give meaning to the phrase ''at random'' in somewhat general situations.