What’s more impossible? Get the better of double Olympic champion Nicola Adams in the ring or selecting 15 great Rio moments, when there are so many to choose from?
Here's some thoughts.
Adam Peaty's smile said it all. As wide as Christ the Redeemer's outstretched arms, it lit up Rio more spectacularly than any carnival as he claimed Great Britain's first gold of the Olympic Games.
And this was a performance worth a day of stifling yawns at work to savour and enjoy, the race starting in the early hours of the morning back home.
Nicknamed 'The Gladiator' by his coach Mel Marshall, the 21-year old ruthlessly slayed all comers and became the first British man to win an Olympic swimming gold since Adrian Moorhouse, 28 long years ago in Seoul.
This was more than a victory - his time of 57.13 seconds took four tenths off the world record he had set in the heats, while he beat his nearest rival, South Africa's Cameron van der Burgh, by over a second and a half.
Surprises are best at the Olympic Games - especially when they are gift-wrapped in gold.
In the space of just 90 minutes, Joe Clarke, Chris Mears and Jack Laugher defied the odds to take K1 canoe slalom and diving’s 3m synchronised titles.
All such moments are emotional of course but for 23-year old Mears it was extra poignant, after live-saving surgery - he was given just a five per cent chance of survival - to remove a spleen ruptured in 2009.
"I still can't really believe that it's happened," Mears said. "I've come from death's door to here. I'm pretty proud.
"When I went into London and competed really well there, that was really emotional for me, because of what had happened to me. London changed me as a person. I became a bit more mature."
Unbeatable but not unbelievable, if there were two people to bet the bank on winning in Rio it was Heather Stanning and Helen Glover.
They like making history - though they claim not to be bothered by statistics and record books.
Four years ago they kickstarted that storied summer with Team GB’s first gold medal and became the first-ever British women to win an Olympic rowing title in the process.
They’ve not lost since, even when Army major Stanning briefly stepped away from the sport for a tour of duty in Afghanistan, Glover maintained their five-year streak with another partner.
There’s an art to exiting the stage and leaving the crowd wanting more and Sir Bradley Wiggins found a way to time it to perfection.
There was a certain inevitability to his final Olympic appearance, as alongside Ed Clancy, Steven Burke and Owain Doull he claimed the team pursuit title in Rio.
It was his fifth career gold and his eighth medal - overtaking Sir Chris Hoy as Britain’s most decorated Olympian in the process.
And what a race it was, as the Australian quarter of Alex Edmondson, Jack Bobridge, Michael Hepburn and Sam Welford seized an early lead that peaked at well over half a second.
But Wiggins and team had a game plan and they stuck to it, though they didn’t overhaul their rivals' advantage until the last 400m of the 4,000m race. For pure and undiluted tension, this will take some beating.
All that glittered was gold as cycling’s first couple showed they simply do not know how to lose.
If Laura Trott and Jason Kenny’s household was a country it would have finished 19th on the medal table, ahead of New Zealand Canada.
Within the space of just over an hour they had secured their place in history, winning their second and third medals of the Games respectively, taking their combined career total to staggering ten.
Kenny’s victory in the men’s keirin was also Great Britain’s 19th of the Games, making this the most successful overseas Olympics in history - with five days still to come. Trott had defended her omnium title earlier in the night.
“Enjoyable isn’t a word I would use to describe it,” she said. “It actually makes me more stressed watching Jason because I’m not in control of it.”
Justin Rose was the ultimate Olympic tourist - and he went home with the best holiday gift ever in his luggage.
Rose gave the impression of being on a fun in the sun break after arriving in Rio. He embraced the opening ceremony like a kid who’d eaten too much sugar, tweeted his view from swimming pool to food hall and left Brazil with an impressive collection of athlete selfies, along with his gold medal.
From striking a hole-in-one in the first round to holding off the challenge of Open champion Henrik Stenson in a thrilling conclusion, Rose has more than played his part and his his sport owes him a debt of gratitude too.
“That felt better than anything I've ever won,” said Rose, who, it should be underlined, was the first English golfer since Tony Jacklin, 43 years previously, to win the US Open with his victory three years ago.
Max Whitlock was the stand-out star of Team GB’s Super Sunday in Rio.
The 23-year-old became Great Britain’s first-ever Olympic gymnastics champion with a score of 15.633 in the floor final at the Rio Olympic Arena, in fact it was the nation’s first medal of any colour on the apparatus.
But he wasn’t done there, returning just over an hour later to collect gold in the pommel horse final with a score of 15.966, just 0.133 ahead of teammate Louis Smith.
"I’ll have a bit of time out from training now but that’s not me done,” he added.
Good news for Tokyo.
Andy Murray is used to the carrying the burden of national expectation, from Melbourne Park to Flushing Meadow and all stops in between.
Perhaps that’s why he loves the Olympics so much, the chance to be just one of the team, rather than the team.
Nine days after he carried the flag at the opening ceremony, he wrapped himself in the flag, after becoming the first man to defend an Olympic men’s singles title in a sizzling final with Juan Martin Del Potro.
Charlotte Dujardin could only manage one sentence to the media before the tears rolled down her cheeks at the Rio Equestrian Centre.
In defending her individual dressage title in Rio on board Valegro, Dujardin became just the second British woman to win three Olympic titles, while also joining Richard Meade at the summit of British equestrian achievements by matching the eventer’s feat across the 1968 and 1972 Games in Mexico and Munich.
But as much as records hold significance in sport, the discipline of equestrian and in particular dressage, revolves around so much more than statistics and medal tallies.
It’s about the intense connection between both rider and horse and the ability for both to work in sync together.
Dujardin and Valegro are head and shoulders above the rest when it comes to such matters.
Nick Skelton became Britain's oldest Olympic gold medallist in any sport, eclipsing shooter Jerry Millner, who won gold in 1908, with his show jumping victory on horse Big Star.
Skelton, 58, claims he is usually mistaken for an ‘athlete's father' when wearing team kit but longevity comes with perks, he always gets a seat on the bus to the Olympic Village.
Only a handful of his Team GB colleagues were born when he made the first of his seven Olympic appearances in 1988 but age hasn't wearied a rider considered as one of the greatest horsemen of all-time.
Along with Big Star, the horse he won team gold on four years ago, Skelton held his nerve in a thrilling jump-off - setting a scorching pace to match the scorching weather and burning off all rivals in the process.
“This year, I have woken up every day in pain.”
Those were pretty much the first words that came out of Alistair Brownlee’s mouth after his historic Olympic triathlon win.
They tell you everything you need to know about the physical sacrifices made by him and brother Jonny to secure their one-two finish in Rio.
The sight of the duo slumped on the blue carpet at the finish line will be one of the defining images of these Games when all is said and done.
The siblings were simply too strong for their rivals and in the end Alistair – as is so often the case – just had too much on the run for his brother, Jonny settling for silver which at the very least is an upgrade on his bronze from London.
We in Great Britain have a fairly uneasy relationship with penalty shootouts – too many times have our national football teams let us down on the big stage.
But here at the Olympics in Rio de Janeiro – Team GB’s women’s hockey team had no such qualms.
The shootout, or ‘shuffles’ to give it its colloquial name, hold no fear for Danny Kerry’s side, for one main reason – they have the best goalkeeper in the world.
Maddie Hinch, playing in her 101st game for her country – was the decisive factor in Team GB’s historic gold medal win over defending champions Holland.
From the moment she swaggered into the ring it was abundantly clear that Nicola Adams was about to make British Olympic history.
The 33-year-old could not have looked more relaxed for her flyweight gold-medal match against France’s Sarah Ourahmoune – flashing her million-dollar smile and shadow-boxing for all the world to see as she bounced onto the canvas in Riocentro.
And once the bell went for the first round, the most decorated boxer in British amateur history was far too classy for her smaller and older opponent who was fighting in her first Olympics.
Adams was a prohibitive favourite coming in – she had won all four past bouts between the two – most recently in April of this year.
However, it is one thing being the favourite and another to go out and deliver her best performance on sport’s biggest stage.
You can’t afford to go out celebrating success in Rio, you run the risk of sleeping through your alarm and missing yet another British gold.
It was not even 9am when Liam Heath secured Great Britain’s 25th gold of the Games with a victory in the fast and furious 200m canoe sprint.
Those British girls with their jolly hockey sticks and Olympic bling hadn’t even got to bed yet.
Heath’s Olympic career has been charting the right trajectory. He followed his bronze, with partner Jon Schofield at London 2012, with a silver medal upgrade in Rio. Now he’s completed the set.
Could it have been anyone else?
The stars aligned in Rio de Janeiro as Mo Farah and Team GB made history– his 5,000m gold taking their medal total to 65.
That number matched their momentous achievement from four years ago in London, and while it was surpassed later that evening as the women’s 4x400m claimed bronze, it was a total few thought would be repeated in Brazil.
After all, no host country has ever improved on their medal tally four years later. But records were made to be broken – and Farah knows all about that.
As a child the 33-year-old preferred Arsenal to athletics, so it was fitting that in Brazil – where football is religion – Farah signed his name into long-distance running legend.
Sportsbeat 2016