38th Putnam 1977 Problem A3 R is the reals. f, g, h are functions R → R. f(x) = (h(x + 1) + h(x - 1) )/2, g(x) = (h(x + 4) + h(x - 4) )/2. Express h(x) in terms of f and g.
Easy h(x) = g(x) - f(x - 3) + f(x - 1) + f(x + 1) - f(x + 3). Other expressions are also true. 38th Putnam 1977 © John Scholes jscholes@kalva.demon.co.uk 30 Nov 1999