In a huge chess tournament, 45 matches were played. Find out how many people were involved if it is known that each participant played one game with every other participant in the tournament.

We have to find out how many people were involved if it is known that each participant played one game with every other participant in the tournament.

Let there are n participants then,

first participant participated with the n-1 participants

now second participant has played with the first participant now he will play with remaining n-2 participants.

similarly, third participant has played with the first and second participant now he will play with remaining n-3 participants.

and so on the second last participant having played with the participants before him will play with the last participant.

We got an arithmetic progression n-1,n-2,n-3,...1

and sum of this is the number of matches i.e.

(n-1)+(n-2)+...+1=45

i.e. (n-1)(n-1+1)/2=45

( since sum of arithmetic progression is number of terms×(first+last term)/2)

i.e. n(n-1)=90

i.e. n(n-1)= 9×10

i.e. n=10

Hence, there are 10 participants