Yan Cui
I help clients go faster for less using serverless technologies.
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Problem
Find the unique positive integer whose square has the form 1_2_3_4_5_6_7_8_9_0,
where each “_” is a single digit.
Solution
| let predicate n = | |
| let nStr = n.ToString() | |
| // make sure n is a 19 digit number | |
| if nStr.Length <> 19 then false | |
| // check the number matches the pattern 1_2_3_4_5_6_7_8_9_0 | |
| else [1..10] |> List.forall (fun i -> int(nStr.[2*(i-1)].ToString()) = i % 10) | |
| // wonderful bit of brute force CPU.. | |
| let answer = | |
| let mutable n = 1000000000L | |
| let mutable squareRoot = 0L | |
| while squareRoot = 0L do | |
| let square = n*n | |
| if predicate square then squareRoot <- n else n <- n+1L | |
| squareRoot |
by Initially I started solving this problem by creating all permutations of 19 digits numbers which fits the required pattern and iteratively square rooting them to find a square root which is a whole number. Unfortunately thanks to rounding errors this approach doesn’t give me the correct answer so I resorted to iterating through the square roots and brute forcing it instead.
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