Why were Los Alamos scientists so confident “Little Boy” would work?

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The 1945 Trinity test was run to prove the complicated “Fat Man” design would even work. But why were scientists so confident of the “Little Boy” design that the didn’t feel the need to do a full test of the design? The design was simpler, but still, no one had ever done it before. Was it purely for time? Lack of materials? Or was the design and principles so sound, it couldn’t fail?

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