## suneja 3 years ago if x represents sum of all the positive 3 digit nos that can be constructed using each of the distinct non zero digits a b c exactly once what is the largest integer by which x must be divisible

1. tcarroll010

There should be a total of 9x8x7 numbers to sum up. Do you agree?

2. tcarroll010

In each of the 3 columns, the numbers 1-9 are equally represented.

3. shubhamsrg

see,,6 nos can be formed using a,b,c now , out of these 6 , a comes 2 times in the first place , 2 times in the 2nd , 2 times in the 3rd same with b and c if we add em all ,, 100(a+b+c)*2 + 10(a+b+c)*2 + (a+b+c)*2 =222(a+b+c) so is the ans 222 ?

4. tcarroll010

So, taking the units column, you can sum 1 x (8x7) + 2 x (8x7) + 3 x (8x7) + ... to 9 x (8x7). Get that sum and add to that a similar treatment for the other 2 columns.

5. suneja

dats rite

6. suneja

@shubhamsrg can u explain y did u pic 100 10.. was lil confuse der

7. shubhamsrg

in base 10 notation, suppose 123, we write it as 100(1) + 10(2) + 3 same for abc 100a + 10b +c

8. suneja

k

9. shubhamsrg

in all those 6 nos. 100a will be there 2 times,,100 b 2 times and 100 c 2 times adding em all,, you get what was written above..