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Sometime around February 2004, a top military official in Iraq estimated that there were about 15,000 total insurgents. About a year later, U.S. military leaders in Iraq announced that 15,000 insurgents had been killed or captured in the previous year.

In private, a skeptical military adviser pointed out to commanders that the numbers didn’t make sense. “If all the insurgents were killed,” he asked, “why are they fighting harder than ever?”