It is a comedy routine as old as the hills, but it afflicts all of us every once in a while. And on Wednesday (September 11) evening, as they prepared to leave Buenos Aires, it afflicted the eighth and ninth Presidents of the International Olympic Committee (IOC).
"You must go first, you are the current President," said Jacques Rogge, or words to that effect.
"Ah, but you have seniority," replied Thomas Bach.
A pregnant pause and then the spirit of Olympic compromise took over. And so it was that the two men headed off towards the same Lufthansa flight to Frankfurt arm in arm. 
They were still together after touching down at around 11am on Thursday morning to be greeted by the first of numerous media posses keen to record the first words of the new IOC President on his return to European soil from the most important IOC Session for at least a decade.
The two men addressed the journalists and camera crews together, perhaps for the last time, before Bach headed off with wife Claudia to the headquarters of the German Olympic Sports Confederation (DOSB) a 15-minute drive away in a dark DOSB Audi.
The DOSB played an important role in the 59-year-old's ascent to the most powerful post in world sport by demonstrating both his vision in conceiving and overseeing its creation via the merger of the Deutsche Sportbund (DSB) and the Nationale Olympische Komitee für Deutschland (NOK), and his managerial capability in acting, since 2006, as its first President.
It was appropriate then that he should tell DOSB staff that they too should take pride in his achievement.
There was time for a lunch of bockwurst before Bach departed for a pre-arranged appearance at the German Sports Ministers' conference, featuring the Federal Minister and counterparts from all 16 regions, in Wiesbaden a 30-minute drive away.
Having played a part in the meeting, Bach was doing yet more media when Volker Bouffier, Christian Democratic Union (CDU) Prime Minister of the state of Hesse, appeared, bearing congratulations for Bach and flowers, embellished with the Olympic Rings, for the absent Claudia, who had already departed for Tauberbischofsheim, the Bachs' home-town, where a reception was planned for that evening.
It was around 6pm by the time Bach himself got back, to be greeted by a crowd in the market square - and an orchestra, one of his favourite metaphors for the Olympic Movement.
On his way into the reception proper, on the second floor of the town hall, 60 fencers from his local club, dressed for action, formed a guard of honour for the man who was one of the members of the winning German foil team at the 1976 Olympics.
This took a while, as Bach stopped frequently to talk to the young athletes, but the new IOC President eventually emerged in the reception room to a surprise: his sister was there with Mayor Wolfgang Vockel to greet him.
A speech from Vockel and a short reply, more homely German fare in the form of meatballs and the evening ended in small talk with the friends and neighbours from this quiet community of 12,000 people who had watched his progress over many years with a great sense of civic pride.
Next day - Friday - brought a trip to Berlin and the first sports competition Bach witnessed as IOC President.
The venue was the Max-Schmeling-Halle, named after the famous boxer, and the occasion, the semi-final of the women's European Volleyball Championship between Germany and Belgium.
Bach was no doubt gratified that the hosts won a close match by three sets to two, after recovering from a two-set deficit. It had evidently occurred to him, however, that his new role sits ill with public displays of sporting patriotism.
He therefore watched with commendable neutrality, applauding outstanding play by both teams.
On Saturday, Bach fulfilled another longstanding engagement with Joachim Gauck, the German Federal President, who had invited him to Schloss Bellevue, his official residence, to help mark the centenary year of the German sport for all movement.
Gauck, who had been the first political leader to congratulate Bach in Buenos Aires, just ahead of Russian President Vladimir Putin, took the opportunity to wish him well in person, saying his election was a historic moment for German sport.
It was at this event that archery became the first sport actually practiced by Bach as IOC President.
Then it was back to Frankfurt for an 11pm appearance on the Sportstudio television programme.
Sunday afforded the first opportunity, apart from, perhaps, the flight back from South America, to take stock and reflect upon what the next eight years might now hold in store.
Today, the whirlwind of activity resumes, with the DOSB board meeting at which he will resign the Presidency, with Hans-Peter Krämer set to step in on an interim basis until the body chooses a permanent replacement in December.
Tomorrow night, Bach will fly to Lausanne, where he is set to spend the rest of the week in and around the IOC's lakeside headquarters.
It is expected to take at least this long just to collate the messages of congratulation that have winged in via just about every communications medium the 21st century has to offer, never mind reply to all of them.
Dieter Graumann, head of the German-Jewish community, is said to be the author of one such message; retired tennis star Steffi Graf of another.
Bach has already said that his first official foreign trip as IOC President will be to Olympia, the Movement's cradle, to attend the lighting ceremony of the Sochi 2014 Olympic flame at the end of this month.