This is a fun - and virtually inconclusive - question. But the killing power of a shotgun is not related to the size of the bore or the velocity of the shot at such a distance. It almost entirely depends on the size/mass of the pellet involved and where that pellet strikes a bird. (Maj. Burrard, decades ago)
Thus, a .410 firing No. 2 shot could indeed kill a pheasant at 100 yards, if that pellet strikes the bird in the right place. No. 6 shot at most any sane muzzle velocity peobably could not.
In all cases, however, it would be a lucky shot. Forward allowance would be staggering.
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