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Square Digit Sum Surmise (Posted on 2015-01-20) Difficulty: 3 of 5
N is a positive integer less than 2015.

Find all values of N such that:
N is equal to precisely 36 less than the square of the sum of digits of N.

***As an extra challenge, solve this puzzle without using a computer program assisted method.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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Hints/Tips answers, only for N<100 Comment 2 of 2 |

solved analytically for 2-digit N=1Oa+b:



getting a=6 if b=4   and a=4 if b=5 

64=(6+4)^2-36     and


did not try for larger numbers, involving 3 unknowns-

leave it to others.

  Posted by Ady TZIDON on 2015-01-20 17:15:54
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