How do you find which row and column a number belongs to in Floyd Triangle

How do you find which row and column does a number belongs to in Floyd Triangle? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55

For example,

• 33 is in the 8th row and 5th column (input 33 → output 8th row, 5th column)
• 46 is in the 10th row and 1st column
• 27 is in the 7th row and 6th column

Thank you so much in advance!

Note that n-th row ends with value n*(n+1)/2. So you can make quadratic equation and solve it to get row number for given number k

n*(n+1)/2 = k
n^2 + n - 2*k = 0
D = 1 + 8*k
n_row = Ceil((-1 + Sqrt(D)) / 2)   //round float value up 

For example, for k=33 you can calculate

   n_row = Ceil((-1 + Sqrt(265)) / 2) = 
           Ceil(7.639) =
           8

Having n_row, find the last number of previous row and position of k in the current row

  n_Column = 33 - n_row * (n_row - 1) / 2 = 
            33 - 28 = 
            5 

Pseudocode for alternative method of row finding:

 sum = 0
 row = 0
 while sum < k do
      row++  
      sum = sum + row