Much Ado About Muffin - or - A Tale of Two Tetrominoes

Ruby awoke with a pounding in her head and chocolate on her breath. What had she been doing last night? As she peeled her forehead from the hard wooden surface it had been resting on, it dawned on her that she wasn’t at home at all, but seated awkwardly at her desk in the Tetris Block Management offices.

Ah yes. The office party.

She conducted a quick forensic analysis. Strewn across the floor were the scattered fragments of broken tetrominoes, empty power-up bars and experimental cheat codes. The theme music was spinning relentlessly between her ears with laboured speed and questionable tuning, and for some reason the air was thick with cake crumbs, floating like pollen grains in the morning sun. Ruby racked her brains to remember. That was it: a friend of hers had been promoted on the day of the party, and to celebrate Ruby had gone on a bit of a baking spree. Well, a baking frenzy. Cake after cake flying out of the office kitchen, all sliced into small squares to fuel the geometric obsession for which Tetris employees are renowned. She noticed she had narrowly avoided sleeping face-down in the half-finished remains of one of her creations. Smiling, she reached for one of the pieces. The chocolate coating had gone rock-solid overnight, fusing the cake into one delicious lumpy mess, but she managed to snap a piece away and chewed recuperatively as the clock struck 9am.

Suddenly her coworker, Howard, burst through the door. He seemed agitated, and not purely by the overpowering fumes of chocolate that to Ruby had become a second oxygen. Relieved to see someone in the office, he rushed over to her desk and stammered:

“There’s an emergency in the warehouse! Someone forgot to bulk-order the tetrominoes” (here Ruby almost choked on her cake) “and there’s nothing left to send the clients! Paul is clamouring for supplies – says someone was up playing all night and reached level 143. What are we going to give him?”

The guilt in Ruby’s head quickly gave way to panic. Paul was already less than pleased with her after Frances had beaten her to the highest turnover last month, and the only thing quicker than his temper was his tetromino drop rate.

“Oh god, what are we supposed to do?” she cried.

She reached down for another consolatory chunk of cake, but stopped herself with a gasp.

“Wait! Howard – what does Paul say he needs?”

“He said he needed that one that’s kind of Z-shaped to send down, and a T-thingy to stick in the ‘coming next’ box.” Howard’s grasp of Tetris terminology was never particularly good, owing to a previous career in the Ministry of Mario Mushrooms. “But why…”

“Shh!” interrupted Ruby, “I’m thinking. Do we still have the paints from that Gameboy Color merger back in the 90s?”

“I think so – why?”

“Because – look! We can pass off pieces of cake as tetrominoes so long as we paint them the right colour, and there’s nine little squares here – more than enough for two tetrominoes! The only question is which one we can do without…” Now that the crisis was partially resolved, Ruby’s mind was eager to return to her improvised breakfast.

“We need to be careful,” she realised. “Only one of the nine configurations produced by removing a chunk will leave us able to cut out a Z and a T, and there’s no hope of sticking any blocks back together once they’re cut.”

Which square can Ruby safely remove?

As Howard scampered away through the cocoa mist, Ruby breathed a sigh of relief and returned to her solitary square of cake. She hoped the client appreciated the sacrifice she had just made. As she went in for another bite, she heard a voice in her ear:

“Ruby! Ruby, wake up! RUBY!”

“Whuhhh…” groaned Ruby. “Where am I?”

It was Howard, shaking her awake with a vigour that, in her opinion, ought to be reserved for baking and baking alone.

“In the office – it’s morning! Paul is livid – he says someone forgot to bulk-order the tetrominoes and there’s nothing left to send the clients! What are we going to do?”

Ruby sat up and noticed that her dream office had almost perfectly represented her present surroundings, except that – disappointingly – the first piece she’d removed from the cake was already gone. Perhaps she had eaten it in her sleep (it wouldn't be the first time). Grumpy, disorientated and feeling like the victim of a lazy plot device, Ruby snapped:

“Well all right, what does he want?”

“Umm… I think he said something about those backwards Ls, or was it the backwards-backwards Ls? Wait – maybe it was tutus, I mean two Ts… or something. All I remember is he wanted two of the same thing!”

Ruby grimaced. Dream-Howard had been far more competent than the real thing, and that was saying something. She dragged her eyes towards the cake, which was exactly as before, except that she was a piece hungrier this time.

“Ok, well it looks like we can manage this so long as he wanted two identical pieces, and the shape was one of those three... are you at least certain about that?”

Howard looked terrified.

“Look – we’re just going to have to hope for the best. There's only one configuration that allows two duplicates to be cut from it anyway. Come to think of it, it allows nothing but pairs of duplicates! I’ll cut out this piece, you take the rest, confirm what he wants then slice it appropriately and slap on the paint, ok?”

Which square does Ruby have to remove this time?

Ruby sat back to begin her breakfast for a second time, but the cake had barely reached her mouth before Howard had returned, wheezing more than ever in the saccharine atmosphere.

“It wasn’t enough – the guy’s still going strong!” he moaned. “This time Paul needs… uh, well he needs… oh no…”

Miraculously, Ruby had opened her desk drawer to find a perfect replica of the previous cake sitting inside. She was only mildly surprised – quantum entanglement was an occasional by-product of serious baking. It was no use scraping Howard’s mushroom-addled brain for more information, and there was no way she was letting a piece of cake go to waste by sending all nine down with Howard. No job was worth that. So she examined the cake closely.

“Ok, well there’s no way to give him any straight lines – the sides aren’t long enough for that – but a line never turns up when you need it anyway. If I remove this chunk you can only get one tetromino out of the resulting shape – that’s no good. There’s no point taking this one out because you’d get the same options and more if you took out this one instead – I guess you could say one set of options is contained in the other. That's true for this other pair of configurations too. Still, six to choose from – I’ll just have to give you the shape that leaves the highest number of combinations. That chunk looks tastiest anyway. Now take it away and write down what he wants next time. You’re a tetromino delivery man, not a waiter at Burger Kong.”

Which was the tastiest-looking square? Which three options did Ruby dismiss? Which combinations of two tetrominoes is it possible to produce?

Ruby stumbled into the kitchen and turned on the oven. As she did so, she felt renewed life rushing through her fingertips and into every fibre of her body. She took a deep, sugary breath and grinned. Today, Tetris needed a baker... and a baker it had.

[Early post this week – I hope you enjoy reading it half as much as I enjoyed writing it! Answers are now available in the follow-up post. Many thanks to Imogen, whose half-eaten cake as pictured above was the inspiration for this post! It was as delicious as the story recollects.]