When two persons receive the same number of points in Olympics, they end up in the same place.
There can be two 1st, two 2nd, two 3rd, three 1st etc. and any combination of these.

For example, 3 participants can be ordered the following ways, where the leftmost is first place:

o	oo	oo	ooo
o	o	 o
o

For x number of people, we can calculate the number of possible combinations:

f(x) = 2^(x-1)

_________________________________________________________________________________________________________________________________
f(2) = 2
o oo
o
_________________________________________________________________________________________________________________________________
f(3) = 4
o	oo	oo	ooo
o	o	 o
o
_________________________________________________________________________________________________________________________________
f(4) = 8
o	oo	oo	oo	ooo	ooo	ooo	oooo
o	o	 o	oo	o	 o	  o
o	o	 o
o
_________________________________________________________________________________________________________________________________
f(5) = 16
o	oo	oo	oo	oo	ooo	ooo	ooo	ooo	ooo	ooo	oooo	oooo	oooo	oooo	ooooo
o	o	 o	oo	oo	o	 o	  o	oo	o o	 oo	o	 o	  o	   o
o	o	 o	o	 o	o	 o	  o
o	o	 o
o
_________________________________________________________________________________________________________________________________
f(6) = 32
o	oo	oo	oo	oo	oo	ooo	ooo	ooo	ooo	ooo	ooo	ooo	ooo	ooo	ooo
o	o	 o	oo	oo	oo	o	 o	  o	oo	o o	 oo	oo	o o	 oo	ooo
o	o	 o	o	 o	oo	o	 o	  o	o	o	 o	 o	  o	  o
o	o	 o	o	 o		o	 o	  o
o	o	 o
o

oooo	oooo	oooo	oooo	oooo	oooo	oooo	oooo	oooo	oooo	ooooo	ooooo	ooooo	ooooo	ooooo	oooooo
o	 o	  o	   o	oo	o o	o  o	 oo	 o o	  oo	o	 o	  o	   o	    o
o	 o	  o	   o
_________________________________________________________________________________________________________________________________
f(7) = 64
o	oo	oo	oo	oo	oo	oo	ooo	ooo	ooo	ooo	ooo	ooo	ooo	ooo	ooo
o	o	 o	oo	oo	oo	oo	o	 o	  o	oo	o o	 oo	oo	o o	 oo
o	o	 o	o	 o	oo	oo	o	 o	  o	o	o	 o	 o	  o	  o
o	o	 o	o	 o	o	 o	o	 o	  o	o	o	 o	 o	  o	  o
o	o	 o	o	 o			o	 o	  o
o	o	 o
o

ooo	ooo	ooo	ooo	ooo	ooo	oooo	oooo	oooo	oooo	oooo	oooo	oooo	oooo	oooo	oooo
oo	o o	 oo	ooo	ooo	ooo	o	 o	  o	   o	oo	o o	o  o	 oo	 o o	  oo
oo	o o	 oo	o	 o	  o	o	 o	  o	   o	o	o	o	 o	 o	  o
						o	 o	  o	   o

oooo	oooo	oooo	oooo	oooo	oooo	oooo	oooo	oooo	oooo	ooooo	ooooo	ooooo	ooooo	ooooo	ooooo
oo	o o	o  o	 oo	 o o	  oo	ooo	oo o	o oo	 ooo	o	 o	  o	   o	    o	oo
 o	  o	   o	  o	   o	   o					o	 o	  o	   o	    o

ooooo	ooooo	ooooo	ooooo	ooooo	ooooo	ooooo	ooooo	ooooo	oooooo	oooooo	oooooo	oooooo	oooooo	oooooo	ooooooo
o o	o  o	o   o	 oo	 o o	 o  o	  oo	  o o	   oo	o	 o	  o	   o	    o	     o