10025 - The ? 1 ? 2 ? ... ? n = k problem
Solution Description : Ad hoc math problem 1 + 2 + 3 + ..... + n = k => n*(n+1)/2 = k => n^2 + n - 2k = 0 So, n = {-1 + sqrt(1+8k)}/2 Using this equation you got the root of n if n*(n+1)/2 equal k then print the root of n Otherwise increment the root of n by 1 until (root*(root+1)/2 - k) is even remember for positive of negative input always output is same output. |
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