The Doctor is playing Monopoly with Mel, winning, and gloating about it, as it isn’t often that he gets to play the role of a power-crazed dictator. However, the game is interrupted when the Doctor notices that the TARDIS is drifting off course. Earlier, while experimenting with the navigational settings, the Doctor accidentally activated the wide-range distress transceiver, and the TARDIS has thus followed an emergency call into the far distant future, the “vulgar end of Time”. In this era, everything has been done, discovered, bought, sold and cheapened, and the Doctor usually avoids it in favour of more interesting times. But the people of Generios One, the capital planet of the Generios system in the constellation of Generios, have sent out a call for help, and the Doctor must respond. However, when he and Mel emerge from the TARDIS they find themselves in the middle of a grand celebration. According to the happily drunken Citizen Sokkery, they have already been saved from the evil alien Skelloids -- by the legendary Time Lord known as the Doctor. As Sokkery lurches off to join a conga line, the Doctor ponders what he’s been told. He’s never visited Generios in his past, and while he can usually sense the presence of his future incarnations when their paths cross, he feels no such sensation this time. So if he isn’t the Doctor who saved Generios, who is?

The Doctor in question is at the Great Council Complex, modestly accepting the accolades of Councillor Potikol. Having used wit and ingenuity to save the system’s seventeen planets from utter annihilation, he now intends to slip away quietly, but his companion Sally-Anne Stubbins points out that they require pluvon power crystals with which to repair the “Stardis”. There are no such crystals anywhere in the system, but after some hesitation, Potikol agrees to give them the cash they need to purchase some elsewhere -- a hundred million credits. Sally-Anne’s Doctor protests and tries to turn down this generous offer, but eventually, reluctantly accepts -- on the understanding that he will repay this loan as soon as possible. Potikol rushes off to arrange the payment... and once he’s gone, Sally-Anne and the “Doctor” drop all pretense to enjoy a good laugh at the gullible planet’s expense. For Sally-Anne and Banto Zame are con artists, and they’ve just pulled their biggest scam yet.

The real Doctor and Mel arrive outside the Great Council Complex, only to find the entrance blocked by a mob of grateful citizens eager to see their saviour the Doctor. Sokkery is here as well, and the Doctor grabs his commemmorative newspaper to check the picture on the front -- of a man the Doctor is certain is not him in any of his incarnations. On his instructions, Mel pretends to faint, and the guards help her and the Doctor into the complex so she can sit down and recover -- but when their guard leaves to fetch Mel a glass of water, she and the Doctor nip off to look for the impostor claiming to be the Doctor.

Potikol has been gone for longer than expected, and Sally-Anne’s starting to become worried, but Banto is sure that Potikol is far too gullible to have figured out the truth. However, when Potikol returns he admits that something has indeed gone wrong; a piece of space flotsam has drifted into the system, and it appears to be interfering with the planet’s computer net, including the links to the Great Bank of Generios. Potikol has sent a Great Space Dredger to destroy the object, and he assures “the Doctor” and Sally-Anne that the matter will soon be taken care of. Sally-Anne fears they’ve been rumbled, but Banto is sure that there’s nothing to worry about. They’re both wrong, as Potikol soon receives terrible news -- the Great Space Dredger has been destroyed...

The Doctor and Mel eventually locate the Great Council Chamber, where they overhear Banto and Sally-Anne discussing their plans to purchase a pleasure planet with their ill-gotten gains. The Doctor bursts in to denounce the impostors, realising what’s going on -- Banto and Sally-Anne travel from planet to planet, staging fake alien invasions, pretending to save the world and hopping it with the reward. Banto concludes that this stranger is just playing the same con, and when Potikol arrives he accuses the Doctor and Mel of being over-excited fans. The guards march the protesting Doctor and Mel out of the chamber, apparently solving Banto’s problem -- until Potikol tells him that the “space flotsam” has destroyed the Great Space Dredger and is heading straight for Generios One. Only the Doctor can save them now!...

At the last moment, the sound stops and a great echoing voice from the alien Cylinder speaks to the people of Generios. Now that it has their full attention, it demands tribute for its alien masters; the people of Generios must give them their three greatest treasures, or the Cylinder will destroy the entire system. They have five marlegs to comply, a period of time which they eventually work out is roughly equivalent to three Generian hours. Banto promises to complete the task, and Potikol leaves to arrange for the Stardis to be brought here so “the Doctor” can leave at once. In fact, Banto believes the Cylinder to be another fraudulent threat, arranged by the stranger in the flashy coat, and he has no intention of letting a poacher drive him off his patch until he’s collected the hundred million credits from his own operation.

The Doctor and Mel have heard the ultimatum as well, as has everybody on Generios One. The Doctor thus uses his cell’s electronic food dispenser to deal with the lock -- although Mel is somewhat disappointed when she learns that his plan is to pick up the dispenser and ram the door open with it. Mel suspects that the mysterious voice may have something to do with the impostors, but the Doctor knows that the technology to generate a corpelectric sound wave is too expensive for such petty criminals to have access to it; the threat is real and something must be done about it. As he and Mel approach the Great Council Chamber, however, they see the guards bringing in the Stardis... and its appearance is the biggest insult of them all.

Potikol and the guards bring the Stardis to the Great Council Chamber, and Potikol gives Banto a list of the system’s three great treasures so he can collect them. In fact, Banto only intends to track down his two competitors and deal with them -- but he’s saved the trouble when they burst back in to resume their confrontation. Banto promises to deal with them himself, and Potikol goes off to address the people, giving the Doctor and Banto the opportunity to lay into each other. Banto is furious that the Doctor is copying his con game, and the Doctor is enraged that his good name is being used to exploit innocent people. And the appearance of the Stardis is the last straw; Banto and Sally-Anne know that the Doctor’s time machine is in the shape of a police box, and they’ve seen pictures of policemen hanging around these things, but their Stardis is not a police box. It’s a portable toilet.

The bickering is interrupted by an angry reminder from the Cylinder that they have only 4.63 marlegs left to complete their task -- and when Banto scoffs at the unconvincing threats, the Cylinder destroys the eleventh planet of the system and fires an energy blast into the Council chamber, right past Sally-Anne’s nose. For the first time, Banto realises that the Cylinder is a genuine alien threat -- and that the time has come for him and Sally-Anne to cut their losses and flee. Realising that the Stardis is in fact a short-range teleporter which Banto intends to use to reach the spaceport, the Doctor and Mel force their way on board in order to reach the TARDIS quickly. Potikol arrives just in time to see the Stardis dematerialise with its characteristic wheezing, groaning, flushing sound...

The Stardis is smaller inside than outside, and conditions are very uncomfortable, particularly when Banto finds that he can’t materialise at the spaceport as he’d hoped. However, the Doctor finds that he can programme the Stardis to materialise in the console room of the real TARDIS, the only journey which the Cylinder is prepared to let them make. As soon as Banto steps out into the TARDIS, he realises that this technology is like nothing he’s ever seen before -- and when the Doctor allows Banto and Sally-Anne to touch his chest and feel the double heartbeats, Banto finally realises that he’s face to face with the genuine article after all. Wanting no more part of this, he hands over the list of treasures and humbly asks the Doctor to let him and Sally-Anne out of the TARDIS -- but the Doctor has already set the co-ordinates and taken off. The Cylinder will permit nobody to leave the system until it receives its tribute, and the Doctor’s going to need help finding the three treasures in time -- and it’s time that Banto and Sally-Anne were taught a lesson. And Sally-Anne can take her hands off his chest now.

The TARDIS materialises in an echoing chamber on the eighth planet, where the first treasure, “Unit ZX419”, is to be found. Banto conducted some research on the Generios system before his arrival, and he knows that there’s something significant about Generios Eight, but he can’t remember exactly what it is. As time is pressing, the Doctor decides to take Sally-Anne to the fourteenth planet to collect the second treasure, while Banto and Mel remain here. Sally-Anne is fine with that; she’s looking forward to spending more time with the real Doctor, although she’s suspicious of the way Banto has been eyeing up Mel. As the TARDIS dematerialises, Banto and Mel start to look around -- but Banto is nervous, and believes that he can see movement in the shadows. If only he could remember what was so significant about the eighth planet...

The TARDIS materialises on Generios Fourteen, which, according to the list, is the home of the next great treasure, Mentos. The Doctor and Sally-Anne emerge into a chilly, rocky landscape, which appears deserted until they hear a distant musical fanfare. As they follow the music to a nearby ruin, the Doctor realises that Sally-Anne is trying to chat him up, and is somewhat taken aback when, unlike most of his companions, she runs out of breath before he does. They arrive at the ruins of a giant ampitheatre to see two figures moving about on a stage; a female asking obscure trivia questions, and a polite elderly man answering them. As the fanfare rings out again, the Doctor realises that the two figures are playing a game...

While Banto apologises to his absent mother for his crimes, Mel tries to convince the hostile Assemblers that they’re on a mission to save the entire system. The Assemblers believe this to be an inefficient organic lie, and only become angrier when Mel admits that they’re here for Unit ZX419, the Assemblers’ greatest achievement. But just as the Assemblers are about to send them both to meet their manufacturer, Assembler One apparently changes its mind and decides to let them take UNIT ZX419 after all... if they can. Mel and Banto get the impression that it isn’t going to be as simple as that. Nevertheless, they have no choice but to agree to the Assemblers’ terms; the Assemblers bring forth Unit ZX419, which to the untrained eye appears to be an unimpressive load of wooden boards, and order Banto and Mel to piece it together. They will be given half an hour to do so; if they fail, they will be disassembled. The Assemblers withdraw to observe their efforts from afar without distracting them, and seal them into the storage bay so they can’t escape. Mel and Banto set to work, and get the first shelf assembled properly... but it vanishes while they work on the next stage of the assembly. And Banto is the first to notice that the instructions seem to be getting longer...

The Doctor and Sally-Anne observe the two figures for a while, and the Doctor eventually works out that the pristine metal box on which the old contestant is standing must be an advanced computer system -- quite possibly Mentos itself. He approaches the figures to learn more, but the fierce female Questioner orders him back to his seat, apparently under the impression that he’s a wayward audience member. The old man, who seems more aware that the entire audience died over 33,000 years ago, answers the Doctor’s questions promptly; he is in fact the real-world interface for the Mentos device, and he’s programmed to answer all questions put to him. The Questioner, however, refuses to let Mentos go until the game is over -- and it’s been going for 330 centuries, as Mentos has never failed to answer a question correctly. The Mentos box is a portal to a shadow universe populated by a team of electronic research devices which can travel anywhere in Time and Space to find the answer to a question; coming on “Superbrain” was meant to be a publicity stunt, but a war broke out between two factions who sought Mentos for their own purposes, and the only people with the codes to shut down the Questioner were killed. When the Doctor impatiently tries to disconnect Mentos, the Questioner blasts him aside with a bolt of electricity; nothing must interrupt the game. The Doctor can’t think of any solution to this problem, but he’s surprised when Sally-Anne promptly gives up all hope; he’s used to his companions bringing him out of his sloughs of despond, rather than sinking in with him. After a few moments’ thought, however, he does come up with an idea after all...

Mel and Banto are slowly coming to realise the truth -- every individual step in the assembly instructions makes sense, but new parts keep appearing, old assembled parts keep vanishing, and the instructions themselves just keep getting longer. These shelves exist in a complex number of dimensions, some of which cannot be perceived by humans; thus, Mel and Banto will never be able to finish putting them together. Mel refuses to give up hope, and tries to inspire Banto by telling him about her family and the Christmas show they used to put on for the pensioners of Pease Pottage. One year, eight feet of snow covered the ground, but the Bushes put their faces to the wind, made it to the church hall and gave the show of their lives. Banto claims that this is the most inspiring tale he’s ever heard, and sets to work with Mel trying to think of a way to delay the Assemblers... although Mel must then admit that although her family put on the show, nobody came to watch it.

The Doctor convinces the Questioner to let him question Mentos, and she agrees to let him place two questions of his own. Unfortunately, before he starts, Mentos reveals that he’s capable of answering logical conundrums which would fox lesser computers, and the Doctor must scramble for a replacement question. He thus asks Mentos the colour of the wallpaper at 35 Jefferson Road in Woking in June 1975, but Mentos answers that question right away. He then asks Mentos what his three wishes were when he blew out his candles on his 900th birthday cake. This one is somewhat tricker, but Mentos answers that question as well -- galactic peace, better control of the TARDIS, and more manageable hair. It seems that later that same day the Doctor was locked in a prison by the evil Mantelli, and carried on a long conversation with his cellmate -- who was another projection of Mentos’ research devices. Mentos really can get anywhere and answer any question in the entire Universe...

The Questioner delivers a devastating putdown and sends the Doctor back to his seat, stunned by his failure. Sally-Anne decides to give it a shot herself, and asks Mentos what she told Banto on the night he asked her to marry him. Unfortunately, it seems that Banto went out drinking the following evening and told everyone who would listen that Sally-Anne had claimed to have mammary enhancement surgery. Enraged, Sally-Anne realises just how hopeless this task is; what doesn’t Mentos know? The Doctor, quick on the uptake, claims that this is her second question -- Mentos must tell them what he doesn’t know. Mentos tries his best, but this is one question he cannot answer, and the game finally ends. Greatly relieved, Mentos shuts down at last, and the Questioner also shuts down after announcing that Mentos has banked a pitiful 679,333,567,010 credits. The Doctor is finally able to disconnect the Mentos box safely, and he and Sally-Anne return to the TARDIS.

With only two minutes left before the Assemblers return, Mel finally realises the truth; since the shelves can never be fully assembled, the Assemblers can’t possibly know what the finished product looks like. And there’s no final picture on the instructions, since the instructions never reach the end. Mel and Banto thus wait for the Assemblers to return, and claim that the Shelves of Infinity are now fully assembled. The Assemblers are quite surprised, particularly when they realise that they’ve got no way of disproving the humans’ claim. They can’t believe that they’ve been outwitted, and insist upon inspecting the Shelves closely; fortunately, at that point the TARDIS returns, and Mel and Banto get the Shelves inside while the Assemblers are checking the assembly instructions. As the TARDIS dematerialises, the Assemblers realise that they’ve been beaten by inferior organic humans. This cannot be possible; therefore, it cannot have happened. Satisfied with this logic, the Assemblers erase the embarrassing event from their memory and return to the important work of making more furniture.

Mel can’t bring herself to believe that the Doctor has been killed at last, and she’s right; he’s been swallowed alive, and after slithering through the jelly’s intestinal tract he manages to local and pummel one of its internal organs, inducing it to vomit him back out. It’s rather upset about this, and about the newcomers’ attempt to steal the diamond -- and says so. When the Doctor realises that it can speak he demands to know why it didn’t just ask him to leave the diamond alone instead of swallowing him whole, and the jelly admits that it’s been alone for millions of years and has almost forgotten how to relate to other people. The Doctor realises that this creature is a Jelloid, one of the longest-lived creatures in the Universe; the diamond’s owners had it sign a fifty-million-year contract to guard the diamond, and it’s already lasted here for thirty million years. It’s actually quite lonely, and has even written a song about it.

Now that the initial misunderstanding has been cleared up, the Jelloid turns out to be quite a pleasant conversationalist, and when the Doctor explains the problem, the Jelloid admits that it’s already heard the Cylinder’s threat and thus agrees to hand over the diamond. However, there’s a problem. In order to retrieve the diamond it will have to switch off the force field pinning it in place, and it’s expecting an important delivery any moment now. It had ordered an entertainment system from Bendelos, but the depot could only specify a delivery time within a range of two million years. It’s already waited one and a half million years, and it’s sure that if it moves away from the teleport unit even for ten minutes, it’ll miss the courier and have to spend the next forty thousand years on hold to arrange another delivery date. Sally-Anne promises to keep an eye out for the courier, and although the Jelloid remains uneasy, it agrees to go and switch off the force field for them.

Meanwhile, on Generios One, Potikol is growing ever more worried. The Cylinder’s deadline is almost up; if the Doctor doesn’t return in fifteen minutes, the system will be destroyed...

The Doctor and Mel leave Banto and Sally-Anne to watch for the courier while the Doctor fetches a clean coat from the TARDIS. Mel remains to power up for a quick departure while the Doctor returns to fetch the diamond, brushing away an annoying insect as he does so. Banto and Sally-Anne are bothered by the same buzzing noise, but they’re more bothered by each other. Banto has failed to make good on any of the promises he made to Sally-Anne, while the Doctor has been nothing but a gentleman -- and, frustrated, Banto now lets slip that all the time he’s been travelling with Sally-Anne, he’s already been married. When the Doctor arrives, the teary-eyed Sally-Anne rushes into his arms, much to his bemusement.

The force field lowers, and as Banto carries the diamond to the TARDIS, the Doctor lags behind to thank the Jelloid. But when it returns, it spots a small plaque lying nearby... announcing that the courier has been and gone. Far too late, the Doctor realises that the buzzing sound was not an insect but a Vecton, one of the fastest-moving creatures in the entire Universe -- and when they failed to respond to its calls, it departed. To make matters worse, Banto then enters the TARDIS with the diamond -- and dematerialises, having observed the Doctor earlier. Now the Doctor and Sally-Anne are stuck on Generios Fifteen with a very angry Jelloid, who’s going to have to spend another twenty million years alone, without its entertainment system -- without even anything to guard. It can use the teleporter to send them back to Generios One, but why should it bother to send away the only company it’s had for millions of years? The Doctor, however, promises that if the Jelloid lets them go, he will use his TARDIS to fetch an entertainment system himself and deliver it here within five minutes of his departure. The Jelloid, quite a reasonable one-celled organism, agrees to these terms. The Doctor and Sally-Anne thus set off for their final confrontation with Banto and the Cylinder...

Mel is furious when she realises what Banto’s done, but although she orders him to return for the Doctor at once, he catches her off guard by claiming that he loves her and asking her to marry him. The TARDIS materialises back in the Great Council Chamber of Generios One, just as the Cylinder’s deadline runs out. Potikol, who was expecting the Stardis instead, is rather surprised by the box which has arrived in its place, but the man he believes to be the Doctor emerges. The real Doctor and Sally-Anne then materialise as well, just in time to “help” Banto present the three great treasures to the Cylinder: the Shelves of Infinity, Mentos, and the largest diamond in all of time and space. The Cylinder accepts this as a suitable tribute, and demands that the Doctor identify himself so he may be rewarded for his efforts. Banto promptly takes centre stage, and, strangely, the Doctor allows him to do so. Mel and Sally-Anne protest and try to explain who the real Doctor is, but the Doctor claims that he’s really Banto Zame, and that the other man is the one, true Doctor. To prove his point, he pulls Sally-Anne into a clinch and kisses her deeply, thus convincing the Cylinder that he can’t possibly be the Doctor of legend. Before Banto can act, the Cylinder ensnares him in a tractor beam, and reveals that it was after the Doctor all along, having picked up the news reports which indicated that he had saved this system from the Skelloids. The quest for the tributes was a ploy, a task which only the real Doctor could have completed. Now that it has positively identified its target, the “Doctor” will be placed in a time bubble and taken to the Cylinder’s homeworld to answer to its masters, the Sussyurats of Chalzon, for his crimes. Banto is drawn away, struggling and protesting in vain, and the Cylinder departs, apologising to the people of Generios for the inconvenience.