It's theoretically possible to win the Tour de France without winning any stages. But has this ever happened?
What about the other Grand Tours (Giro d'Italia, Vuelta a España)?.
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Sign up to join this communityYes it has in fact happened several times, the most recent ones being 2017 (Chris Froome), 2006 (Óscar Pereiro after Floyd Landis was disqualified) and 1990 (Greg LeMond). Before that, the TdF was also won without a stage victory in 1922, 1956, 1960 and 1966. (see here).
For your second question, Wikipedia has a list for the
Giro (1913, 1946, 1951, 1961-63, 1969, 1971, 1999, 2002, 2008, 2011, 2012, 2015)
and the Vuelta (1955, 1965, 1971, 1976, 1990, 2001, 2009, 2010, 2015).
(To keep to the same format, here's the TdF again): 1922, 1956, 1960, 1966, 1990, 2006, 2017.
So, the Giro has been won 14% of the time by someone who didn't win a single stage, while for the Tour this has only happened in about 6% of cases. For the Vuelta, it's close to 13%.
It might be possible because the overall winner has to have the best total time. The most plausible way to achieve this is if Clever arrives behind other riders in each stage and if those riders (do him the favour to*) lag behind in the following stages their total time will be higher than the time of Clever. Making him the overall winner. All he needs to do is remain as far in the front as possible.
This year's (2017) overall winner of the TdF, Chris Froome, didn't win a single stage. Which means that the answer is yes!