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In a game of Magic, I attack with a 5/5, indestructible, trample. My opponent blocks with a 2/3 and a 2/2.
He hopes the 2/2 will die because of an effect when that creature dies.
Can I choose to just sink my five damage into the first creature and not touch the second
You can always assign more than lethal damage to a creature. In your example, you can assign five damage to the 2/3 and not touch the 2/2.
510.1c A blocked creature assigns combat damage to the creatures it’s blocking. If it isn’t currently blocking any creatures (if, for example, they were destroyed or removed from combat), it assigns no combat damage. If it’s blocking exactly one creature, it assigns all its combat damage to that creature. If it’s blocking two or more creatures, it assigns its combat damage to those creatures according to the damage assignment order announced for it. This may allow the blocking creature to divide its combat damage. However, it can’t assign combat damage to a creature that it’s blocking unless, when combat damage assignments are complete, each creature that precedes that blocked creature is assigned lethal damage. When checking for assigned lethal damage, take into account damage already marked on the creature and damage from other creatures that’s being assigned during the same combat damage step, but not any abilities or effects that might change the amount of damage that’s actually dealt. An amount of damage that’s greater than a creature’s lethal damage may be assigned to it.
The Judge's Corner has a great video that covers the specific scenario in your question and more.
Yes, per 510.1c, quoted below in its entirety with emphasis added.
510.1c
A blocked creature assigns its combat damage to the creatures blocking it. If no creatures are currently blocking it (if, for example, they were destroyed or removed from combat), it assigns no combat damage. If exactly one creature is blocking it, it assigns all its combat damage to that creature. If two or more creatures are blocking it, it assigns its combat damage to those creatures according to the damage assignment order announced for it. This may allow the blocked creature to divide its combat damage. However, it can’t assign combat damage to a creature that’s blocking it unless, when combat damage assignments are complete, each creature that precedes that blocking creature in its order is assigned lethal damage. When checking for assigned lethal damage, take into account damage already marked on the creature and damage from other creatures that’s being assigned during the same combat damage step, but not any abilities or effects that might change the amount of damage that’s actually dealt. An amount of damage that’s greater than a creature’s lethal damage may be assigned to it.
You announce the damage assignment order for the blocking creatures, putting the 2/3 first and the 2/2 second. Assign 5 damage to the 2/3, leaving 0 damage to be assigned to the 2/2.
Since your 5/5 has trample, briefly look at 702.19.b. Since lethal damage hasn't been assigned to each creature that blocked it, you can't assign damage to their control.
Yes. You can assign as much damage as you want to a single blocker. The only restriction is that you cannot assign damage to a second blocker until you have assigned lethal damage to the first.
510.1. First, the active player announces how each attacking creature assigns its combat damage, then the defending player announces how each blocking creature assigns its combat damage. This turn-based action doesn’t use the stack. A player assigns a creature’s combat damage according to the following rules:
510.1a Each attacking creature and each blocking creature assigns combat damage equal to its power. Creatures that would assign 0 or less damage this way don’t assign combat damage at all.
510.1b An unblocked creature assigns its combat damage to the player or planeswalker it’s attacking. If it isn’t currently attacking anything (if, for example, it was attacking a planeswalker that has left the battlefield), it assigns no combat damage.
510.1c A blocked creature assigns its combat damage to the creatures blocking it. If no creatures are currently blocking it (if, for example, they were destroyed or removed from combat), it assigns no combat damage. If exactly one creature is blocking it, it assigns all its combat damage to that creature. If two or more creatures are blocking it, it assigns its combat damage to those creatures according to the damage assignment order announced for it. This may allow the blocked creature to divide its combat damage. However, it can’t assign combat damage to a creature that’s blocking it unless, when combat damage assignments are complete, each creature that precedes that blocking creature in its order is assigned lethal damage. When checking for assigned lethal damage, take into account damage already marked on the creature and damage from other creatures that’s being assigned during the same combat damage step, but not any abilities or effects that might change the amount of damage that’s actually dealt. An amount of damage that’s greater than a creature’s lethal damage may be assigned to it.
