P.o.t.W. #14 Solution
(a) Let the total number of coins in the well at time \(t = n be S. Then, \(1 + 2 + 3 + \ldots + \left( {n - 2} \right) + \left( {n - 1} \right) + n = S (1) This can be re-written, such that \(n + \left( {n - 1} \right) + \left( {n - 2} \right) + \ldots + 3 + 2 + 1 = S (2) \(\left( 1 \right) + \left( 2 \right) gives:...