this is still the most perplexing aspect for me. I have read several analysis' of this and still cannot get a satisfactory answer. The sun made me do it isn't enough for 1 shot---hesitation, then 4 more shots.
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Indeed this is a problem with many possible interpretations, but I'd recommend invoking Camus' own idea of "rebellion" here. The sun is the famous "absurd reason" for murdering the Arab, but remember that Camus does not advocate a quite resignation to the absurd. On the contrary, he urges us to fight and rebel against it--carving out a meaning for ourselves. I think it's possible that this act of shooting the Arab four additional times might represent a frustrated attempt to do just that.