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Summing the factorials (Posted on 2014-03-15) Difficulty: 3 of 5
1.Please list all the squares, below 6000, that are the sum of three distinct factorials.
2.Same task, without the "distinct" condition.

No Solution Yet Submitted by Ady TZIDON    
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Solution computer solution | Comment 1 of 3
Since 8! is greater than 6,000, we only need to check sums that involve factorials of digits up to 7.  The following checks for part 1:

squares = []
for a in range(6):
for b in range(a+1,7):
for c in range(b+1,8):
f = factorial(a) + factorial(b) + factorial(c)
if sqrt(f) == floor(sqrt(f)) and f not in squares:
squares.append(f)
print a, b, c, f

and produces:

0 1 2 4
0 2 3 9
0 5 6 841
4 5 7 5184

For part 2, a simple tweak to the code checks without the distinct condition and produces two more results:

0 0 2 4
0 2 3 9 
0 4 4 49
0 5 6 841
3 3 4 36
4 5 7 5184

  Posted by tomarken on 2014-03-15 11:02:55
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