ruby - Test works, but it's too slow for the test -

hi guys spent while pairing partner solving problem https://www.codewars.com/kata/playing-on-a-chessboard/train/ruby

it passes every test has stderr @ end saying:

process terminated. took longer 12000ms complete. 

can please advise on how speed following code or make more efficient?

def game(n)   # lowest common multiplier   mult = (1..2*n).to_a.reduce(1,:lcm)   y = 1   x = 1   # numerator sum   numsum = 0    while y <= n     while x <= n       #        numsum += x * mult / (x + y)       x += 1     end     x = 1; y += 1   end    array = [rational(numsum, mult).numerator, rational(numsum, mult).denominator]   if array[1] == 1     [array[0]]   else      array   end  end 

note following part of code:

while y <= n   while x <= n      numsum += x * mult / (x + y)     x += 1   end   x = 1; y += 1 end 

note have 2 nested loops, each 1 n iterations.
means code has complexity of o(n²) (you can read here).

thus, if call game function high value of n, code may hang.

i suggest try rethink algorithm.
exists more efficient way solve problem.