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The description for splash weapons says:

A hit deals direct hit damage to the target, and splash damage to all creatures within 5 feet of the target.

Does that mean that it hits a 3x3 area, or a plus sign? Are diagonals included? I know for the purposes of movement, moving diagonally once only counts as five feet.

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Yes, you include the diagonals, because the diagonals are within five feet.

When calculating distance along diagonals, one uses a “5, 10” alternating scheme: the first diagonal square is within 5 feet (and therefore within the splash), the second diagonal square is 10 feet beyond that (i.e. 15 feet), so it would not be within a 10-ft. splash, e.g. stink bomb.

The section on Throwing a Splash Weapon has more details.

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