Tournament@Moon!!Number Theory Level pending
The Green Alien breed residing deeply under the surface of the Moon is organising a huge MIDE Rated Chess Tounament. These dwarf living beings have a large population( \(123456789\) ) and all of them are participating!! The chess committe has adjusted some rules such that there are no draws ever. In order to find out the time it would take to finish off the whole tournament the Prime Minister orders you, the most reputed mathematician of the "planet", to find out the exact number of matches it would take to have a winner and warns to throw you off to the sun if the answer you give to him turns out to be wrong!!!
What is the answer you gave him?