Since there are two players per match, at first 32/2 = 16 matches will be held( half of them will be eliminated in knock out) 16winners would play 8 matches against each other. 8 winners would play 4 matches against each other and so on. To put together, the number of matches played will be 16+8+4+2+1 =31matches. This exactly matches the data in question. So my assumption is 32 players is correct.

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If n players play: 
At the first level  there are n/2 matches, next level n/4 matches, next level n/8. and so on until there is just one match.
matches = 1+ 2+ ..+ n/4 + n/2  =>  initially there are n players in the tournment. After first round of n/2 matches there are n/2 players to play next round. In the next round n/4 players.
Number of matches total 31 =  1+  2 +  4 +  8 +  16  = 1 + 2  + 2^2 + 2^3 + 2^4
Initial first round there were 2^4 = 16 matches=>  32 players were there.