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When Kuldotha Flamefiend enters the battlefield, you may sacrifice an artifact. If you do, Kuldotha Flamefiend deals 4 damage divided as you choose among any number of targets.
If some of the targets become illegal for Kuldotha Flamefiend's ability, the original division of damage still applies, but the damage that would have been dealt to illegal targets isn't dealt at all. If all of the targets become illegal, you can't sacrifice an artifact.
You divide the damage as Kuldotha Flamefiend's triggered ability is put onto the stack, not as it resolves. Each target must be assigned at least 1 damage. You can't choose more than 4 targets and assign 0 damage to a target.
You don't choose whether to sacrifice an artifact or which artifact you're sacrificing until the ability resolves. Once you decide to sacrifice an artifact (or not), it's too late for players to respond.
You may choose zero targets. If you do, Kuldotha Flamefiend deals no damage, but you may sacrifice an artifact.
