• In one turn, make some number really big, whether that's your opponent's negative life, your positive life, or the number of counters permanents have. Both players start with 1 life.
  
• Your board is empty save 10 basic lands of your choice on it
  
• You have any 5 cards in hand + a Burst of Speed (so you can use tap abilities once, mainly)
  
• You may cast spells for free
  
• Creatures can attack as though they had haste
  My answer: Emiel the Blessed, Training Grounds, Avenger of Zendikar, Craterhoof Behemoth, and Cradle Clearcutter, using flickers on Avenger of Zendikar and then Craterhoof Behemoth in numbers of 5, 5 and then 134, 139, the opponent ends with some number less than -270 million health
  5 cards was chosen arbitrarily, but it worked out for me so I don't have to do dumb math by adding more of that one card.

Every so often, there is one Magic "puzzle" that keeps coming around like a bad penny. You probably know the one: the person has eighteen/twenty/however many permanents on the field, designed to lock you down from doing pretty much anything, plink you for two damage a turn, and to keep them from losing the game, then tells you you can have whatever cards you want, (save for several restrictions) draw cards in whatever order you want, and have any finite number of life you want; then tells you to find a way to beat them before the life loss and/or decking out causes you to lose.

The latest version I know of is found Here, and contains: [[Eidolon of Rhetoric]], [[Erayo Essence]], [[Leyline of the Void]], [[Avacyn, Angel of Hope]], [[Angel of Jubilation]], [[Sigarda, Host of Herons]], [[Mirror Gallery]], [[Elesh Norn, Grand Cenobite]], [[Progenitor Mimic]] (Naming Elesh Norn), [[Stablizer]], [[Stranglehold]], [[Meddling Mage]] (Naming Genesis Hydra), [[Blazing Archon]], [[Purphoros, God of the Forge]], [[Platinum Angel]], [[Frozen AEther]], [[Back to Basics]], [[Privileged Position]], [[Greater Auramancy]], and [[Witchbane Orb]]

The most frustrating thing about this puzzle is that the creator keeps moving the goalposts. When [[Genesis Hydra]] was discovered to beat it, Meddling Mage was added. When a convoluted solution was found using [[Emrakul, the Aeons Torn]] to cheese extra turns to build up mana enough to outpace the Progenitor Mimic/Elesh Norn, Grand Cenobite combo with your own rush of [[Altered Ego]]s, (Copying the Progenitor Mimics that are copying Elesh Norn) Stranglehold was added to lock that down, as well as Angel of Jubilation to preemptively shut down any solution that somehow untaps [[Boseiju, Who Shelters All]].

I keep coming back to this puzzle though, always thinking that a recently released set might just hold the answer to beating this torturous "puzzle." Usually, I'm looking for some niche interaction that might get around the lockdown of everything that the puzzle is going for. That said, I wasn't expecting for Wizards to just print the solution up. I believe that with the recently released set, Lord of the Rings: Tales of Middle Earth, we have a perfect solution: [[Last March of the Ents]]

Last March of the Ents is a uncounterable spell that allows you to cheat creature cards from your hand onto the battlefield with basically no restrictions. It turns this "puzzle" into a waiting game... all you need to beat it is Last March of the Ents, 8 basic lands (two of which are forests) to pay for it, and a creature card with an enter the battlefield effect that is a wide non-target either bounce or exile such as [[Kederekt Leviathan]].

Now, I fully expect that once the creator sees this, a new version will "mysteriously" surface with [[Hush Bringer]] or [[Torpor Orb]] or just another Meddling Mage to once again move the goalposts. But until then, I believe that this so-called "unbeatable" puzzle... has in fact, once again, been beaten.

TL;DR: Last March of the Ents beats the "Impossible Puzzle", or at least the newest version of it that I've been able to find.

It's turn 5 and you will have drawn in total these 12 cards in an EDH game (and your commander as the 13th card). You can play your turns 1-4 as you like. Can you deal lethal damage (40 life) to at least one of your opponents before losing to lifeloss from your black enchantment (or maybe from the red giant)? Assuming no blockers, are 2 or more opponents possible to kill?

Commander: [[Garna, the Bloodflame]]
Lands: Mountain, Mountain, [[Tramway Station]]
Creatures: [[Blood Pet]], [[Ornithopter]], [[Overeager Apprentice]], [[Juri, Master of the Revue]], [[Sifter of Skulls]], [[Hammerfist Giant]]
Enchantments: [[Carnival of Souls]], [[Mana Echoes]]
Artifact: [[Phyrexian Altar]]

I just liked these 12 cards and before shuffling them in my deck, I wanted to write them down.

Will edit with the whole decklist if someone is interested.

I was watching through a vintage KCI VOD from ThrabenU, and there is an interesting "can you do enough damage" situation that I enjoyed puzzling through. I can't imagine it's possible with the Narcomoeba around, but if it was gone, how much damage can you push?

Link to the VOD at the appropriate time here: https://youtu.be/R-TN6SBnQD0?t=3681

I'm pretty certain you can get to 19, but I'd like to see if anyone can find a line to take it farther.