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The paragraph is poorly worded, yes. What it was trying to say is that the gun type design didn't work with Plutonium, but they concluded that it would work with Uranium and didn't bother detonating one first.

Whether any of them actually worked is a matter for another debate, but this isn't the contradictory statement you think it is.

Nukes are fake n gay. If they were real, India would have nuked Pakistan already, or vice-versa. The Japan bombs were fuel/air, we had an extensive firebombing campaign in Japan. Most of their houses and buildings were made of wood and ricepaper. The Japs rebuilt Hiroshima and Nagasaki immediately after the war, there is no radiation. Most of 'history' is a lie.