Permutation of digits | 5-digit number

 
 

132,   264,   396 ;

132   =   (13+31)   +   (32+23)   +   (21+12)
264   =   (26+62)   +   (64+46)   +   (42+24)
396   =   (39+93)   +   (96+69)   +   (63+36)

 
 

Now, find a 5-digit number, with distinct nonzero digits, which is equal to the sum of all the different 3-digit integers formed by the three digit permutations of its five digits.

 
 
 
35964.   with the 3 digit permutations

{359,356,354,395,396,394,365,369,364,345,349,346}
{539,536,534,593,596,594,563,569,564,543,549,546}
{935,936,934,953,956,954,963,965,964,943,945,946}
{635,639,634,653,659,654,693,695,694,643,645,649}
{435,439,436,453,459,456,493,495,496,463,465,469}

 
Solved by Paul.
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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2 Responses to Permutation of digits | 5-digit number

  1. paul says:

    That would be

    35964. with the 3 digit permutations.{359,356,354,395,396,394,365,369,364,345,349,346,539,536,534,593,596,594,563,569,564,543,549,546,935,936,934,953,956,954,963,965,964,943,945,946,635,639,634,653,659,654,693,695,694,643,645,649,435,439,436,453,459,456,493,495,496,463,465,469}.

    Paul.

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