If you think you've solved it, or if you're stuck, email pi3challenge@sheffield.ac.uk or tweet to @pi3challenge

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A square number is one that can be written as the square of another number. For example, 9 is a square number, because 9 = 3² = 3 x 3.

An example of a number with all the digits once only is 9586714230. But this is not a square number. An example of a number with all the digits once only which is also a square number is 1532487609 = 39147².

Hint #1 : Whereas Challenge #1 needed some subtle mathematical reasoning, this challenge just needs your programming skills.

Hint #2 : The str, set, and len functions are very useful for this problem. Take a look at this page on lists, strings and sets. Find out how a number can be turned into a string which can then be turned into a list or set.

Extra challenges:

• How many prime numbers can be written as N+1, where N is a square number with all digits.
• How many prime numbers can be written as N-1, where N is a square number with all digits.  Is this just coincidence, or can you find an explanation?
• How many of the roots n of these square numbers, n^2 = N, are themselves prime numbers? Coincidence, or can you find an explanation?
  
• How many permutations of the digits 9876543210 are there? How many of these are valid numbers? What proportion of such numbers are square numbers?
  
• Can you find an example of a number whose square contains each digit exactly twice?