Pandigital Squares
September 29, 2020
A pandigital number, like 4730825961, is a ten-digit number in which each digit from zero to nine appears exactly once. A square number, like 25² = 625, is a number with an integral square root.
Your task is to write a program that finds all of the pandigital square numbers. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.
Programming Praxis 
Cute little exercise. Here is my take on it in Julia 1.5: https://pastebin.com/XV0aiT9j
Please excuse the unnecessary use of semicolons here. I’ve gotten into the habit of using them everywhere, ever since I started learning another language that requires them. Cheers!
No need to test all integers from 35000 to 100000. Since all pandigitals are divisible by 9, we only need test integers divisible by 3 and exclude those ending in 0
@Ernie. Good point! I’ve amended my code to take into account this information. Thank you for the tip!
Here’s a solution in C.
#include <stdbool.h> #include <stdint.h> #include <stdio.h> #include <stdlib.h> #define MIN_PANDIGITAL 1023456789 #define MAX_PANDIGITAL 9876543210 static bool is_pandigital(int64_t x) { if (x < MIN_PANDIGITAL || x > MAX_PANDIGITAL) return false; int count[10] = {0}; for (int i = 0; i < 10; ++i) { int r = x % 10; if (++(count[r]) > 1) return false; x /= 10; } return true; } int main(void) { int start = 31991; // int(sqrt(MIN_PANDIGITAL)) int end = 99380; // int(sqrt(MAX_PANDIGITAL)) for (int x = start; x <= end; ++x) { int64_t square = (int64_t)x * (int64_t)x; if (is_pandigital(square)) printf("%ld\n", square); } return EXIT_SUCCESS; }Output:
Here’s a solution in OCaml.
let is_pandigital x = let min = 1023456789 and max = 9876543210 in if x < min || x > max then false else let rec is_pandigital' pending observed = if pending = 0 then true else let digit = pending mod 10 in let mask = 1 lsl digit in if (mask land observed) > 0 then false else is_pandigital' (pending / 10) (observed lor mask) in is_pandigital' x 0 ;; let start = 31991 and finish = 99380 in let rec loop i = if i > finish then () else let square = i * i in if is_pandigital square then Printf.printf "%d\n" square; loop (i + 1) in loop startOutput:
Some Golang, very zippy so I didn’t make any extra optimizations: https://pastebin.com/bJwdAHw9