## suneja 2 years ago if x represents the 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, wat is the largest integer by wic x must be divisible?

1. suneja

no its 222

2. matricked

see it is clear for the sum of all 3-digited number is always divisible by 111

3. matricked

total no. of 3 digited nos as per ur question is 504 do u need the highest integer which divides the sum of all 504 numbers? or something else..

4. matricked

if i am not wrong the sum of all 3 digited numbers is 279720 with each of the distinct non zero digits a,b,c exactly once it is divisible by integers greater than 222

5. matricked

?? r u there

6. suneja

how did u gt tis?? .. bit confused

7. matricked

see in any order the each digit 1 through 9 will appear as many as(8X7) times in the unit , tenth and hundredth place

8. matricked

now the sum of 1 through 9=45 hence required sum of all reqd + 3digited number is=45*56*(100+10+1)=279720

9. matricked

i hope it is clear to u or point where i am making mistake

10. suneja

see u might be rite but its jst not helping.... no offense but see its 3digit no so it shud be 9X8X7 Possibilities

11. matricked

yes u r correct that is total 504 numbers possible

12. suneja

k then

13. matricked

now each of the digits appear 504 /9 =56 times in each column

14. matricked

do u agree

15. suneja

k

16. matricked

now can u guess the sum total of each of the three columns

17. matricked

will it not be 56*(1+2+3....+9)=56*45=2520

18. matricked

am i correct...