How to determine the number based on the result?

Question

Mathematics

You need to write a function that takes n number of games as input and gives the number of teams at which exactly n games will be played

input: n - games played
output: n - teams that played exactly n games - games

are played in 2 stages:
1 - teams are divided into pairs and play for elimination until an odd number of teams remain (maybe more than one game)
// then just divide by 2 until an odd number of teams remain

2 - if there are more than 1 team left, you need to play games between all possible pairs of teams
// formula n(n - 1) / 2

I sort of figured out how to calculate the number of games based on the number of teams, but I can't figure out how to do the opposite, calculate the number of teams based on the number of games

Answer 1

Let your number of teams be p * 2 ^k , where p is odd.
Then the total number of games will be p*(2 ^k - 1) + p*(p - 1)/2 and this is equal to n - the input parameter.
You need to find such p and k for this equality to hold.
The formula shows that n must be divisible by p , so just iterate over all the divisors of n , calculate k and check that k is an integer.