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Positive Integer and Power Puzzle (Posted on 2015-08-10) Difficulty: 3 of 5
N is a 6-digit positive integer whose sum of digits is 43.
Determine N, given that precisely one of the following statements is false:
  1. N is a perfect square
  2. N is a perfect cube
  3. N < 500000

No Solution Yet Submitted by K Sengupta    
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Solution computer solution Comment 2 of 2 |
The following Python program finds:  499849
as the sole solution

def sod(n):
    """ Input an integer.  Returns the Sum of the Digits  """
    aList = list(str(n))
    ans = 0
    for c in aList:
        ans = ans + int(c)
    return ans

for n in range(100000,1000000):
    if sod(n) != 43:
        continue
    score = 0
    if round(n**(1/2))**2 == n:
        score += 1
    if round(n**(1/3))**3 == n:
        score += 1
    if n < 500000:
        score += 1
    if score == 2:
        print (n)
  Posted by Larry on 2020-07-06 07:12:55
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