Butterfly (strategy using options) and Arrow-Debreu Securities

Assume that the only state variable is the S&P500 index levels. Assume that you have a continuum of strike prices of options over the S&P500 index. Show how to construct a state contingent claim that pays $1 in a given state (say, S&P500 is at 1500 a year from now). This is a question discussed in Prof. Rubinstein's lecture.