Four digit numbers are formed by 4 different digits a,b,c,d( where none is zero) without any repetition of digits. prove that the sum of all such numbers when divided by the sum of the digits a,b,c,d gives the quotient 6666.

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- October 8th 2012, 01:35 AMgeniusgarvilproblem!!!!!
Four digit numbers are formed by 4 different digits a,b,c,d( where none is zero) without any repetition of digits. prove that the sum of all such numbers when divided by the sum of the digits a,b,c,d gives the quotient 6666.

- October 8th 2012, 04:44 AMStefanTMRe: problem!!!!!
Hi,

the digits a,b,c,d are the form:

10^3*a+10^2*b+10*c+d

Because all digits cann take the I, II, III or IV position, there are 24 number (24= 1*2*3*4, permutations).

Add together this 24 numbers, and see...