This is just another example of a problem I decided to attempt as a break at work, trying to form the solution before the cookie on the Project Euler site ran out.

## Problem

It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order.

Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits.

## Python Solution

This could be written in C or Cython to perform much more quickly, and I’m sure there are other optimizations that could be made to this code, but this was written and executed in a total of about three minutes using the Sage Notebook.

import time start = time.time() def numDigits(n): r""" return a sorted list of digits in a number """ L = [] while True: L.append(n % 10) n /= 10 if n == 0: break L.sort() return L i = 1 while True: a = numDigits(i) for j in range(1,7): b = numDigits(i * j) if a != b: break if j == 6: print i i = 0 if i == 0: break i += 1 elapsed = time.time() - start print "result found in %s seconds" % elapsed

When executed, we find the following result.

142857 result found in 1.92401385307 seconds

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