The Problem of God's Retribution

How do we reconcile what we know of God's mercy and forgiveness with his command in 1 Samuel 15:3 to "utterly destroy" the Amalekites, a command which includes not sparing even women, infants, and young children?

This is the problem of God's retribution, and it has been a stumbling block to so many, causing them to see God as capricious and vindictive. But a closer look at the text reveals quite the opposite.