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One of my players is playing an alchemist and he plans on combining the alchemist's Int damage bonus for bombs with focused shot. Both add your Int mod to damage, so does that count as the same source? Would this be the same as a bow and arrow with their enhancement bonuses? To use the feat he plans on taking the discovery which lets him add a bomb to a bolt or arrow.

Alchemist Bomb

On a direct hit, an alchemist's bomb inflicts 1d6 points of fire damage + additional damage equal to the alchemist's Intelligence modifier.

Focused Shot

As a standard action, you may make an attack with a bow or crossbow and add your Intelligence modifier on the damage roll.

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No, they are not from the same source.

Bonuses without a type always stack, unless they are from the same source.

The fact that both modifiers base on Intelligence doesn't mean, that the source is the same. There are two sources: class feature Bomb and feat Focused Shot.

Of course, as you mentioned Explosive Missile discovery must be made.

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  • \$\begingroup\$ Note that, even when using Explosive Missile, the 2 int mods don't even modify the same dice rolls. You will have the normal ranged weapon damage (+ int from focused shot) and the bomb damage (+ int from basic rules). They will happen at the same time, but if, for example, the target has resistance to fire, it won't affect the ranged weapon damage, only the bomb damage. \$\endgroup\$ – GreySage Jun 13 '16 at 2:46

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