explain why calculation step by step

Consider an investor that needs to cover a liability of $1,000 in two years from now. He can invest into (i) a one year discount bond and (ii) a three year pure discount bond both having a face value $100. Assume that the yield to maturity is 10%. How many units of the three year pure discount bond does the investor need to purchase to be able to cover the liability of $1,000 for sure even if the yield to maturity changes in the second year? (a) 10 (b) 5.5 (c) 4.13 (d) 0.5