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rvc

  • one year ago

Hom many non-negative integers less than 10,000 are there such that the sum of the digits of the number is divisible by 3?

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  1. rvc
    • one year ago
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    The options are A. 1112 B. 2213 C. 2223 D. 3334

  2. math&ing001
    • one year ago
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    Hint: If a number is divisible by 3, the sum of its digits are divisible by 3 and the other way round works too.

  3. rvc
    • one year ago
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    i know that but how will i find the sum?

  4. math&ing001
    • one year ago
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    I was hoping you'd figure it out yourself. Solve 3k<=10,000 for k, with k a natural number.

  5. rvc
    • one year ago
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    Ah i have to solve 3k=10,000?

  6. math&ing001
    • one year ago
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    Yep

  7. rvc
    • one year ago
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    3333.3333

  8. rvc
    • one year ago
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    but how u figured?

  9. math&ing001
    • one year ago
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    Yeah that's why I put the inferior sign, round it to the inferior natural number.

  10. ikram002p
    • one year ago
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    well sum of the digits divisible by 3 means the number itself divisible by 3

  11. mathmath333
    • one year ago
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    does it includes 0

  12. rvc
    • one year ago
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    @ikram002p please explain

  13. ikram002p
    • one year ago
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    so 3,6,9,.......,9,999 all are divisible by 3 and there sum of digits is divisible by 3 as well

  14. rvc
    • one year ago
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    yep

  15. math&ing001
    • one year ago
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    Here's an example 18 is divisible by 3 : 1+8 = 9 is divisible by 3.

  16. ikram002p
    • one year ago
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    :) so u can count them now ?

  17. mathmath333
    • one year ago
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    read the divisiblity for 3 here https://en.wikipedia.org/wiki/Divisibility_rule

  18. ikram002p
    • one year ago
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    here is a trick 3,6,9,.......,9,999 = 3*(1,2,3,......,1111)

  19. ikram002p
    • one year ago
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    ps:- dont forget the zero ;)

  20. mathmath333
    • one year ago
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    actually that equals 3333 from \(3,6,\cdots\ 9999\)

  21. ikram002p
    • one year ago
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    oh sorry i made a typo :P

  22. ikram002p
    • one year ago
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    so it would be 3333+(Zero count 1)=3334

  23. ikram002p
    • one year ago
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    it says sum of digits divisible by 3 not equal 3 3|0

  24. rvc
    • one year ago
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    :/

  25. rvc
    • one year ago
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    ikky i get ur explanation 3(1,2...) 3k

  26. ikram002p
    • one year ago
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    so now u can count them ?

  27. ikram002p
    • one year ago
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    i made a typo first here 3,6,9,.......,9,999 = 3*(1,2,3,......,3333)

  28. ikram002p
    • one year ago
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    and dont forget to add the zero :D

  29. rvc
    • one year ago
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    yay got it :*

  30. ikram002p
    • one year ago
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    good :D

  31. rvc
    • one year ago
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    Thank you so much to @ikram002p @Loser66 @mathmath333 @math&ing001 and that unknown user(i know who is it)

  32. ikram002p
    • one year ago
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    you are the most welcome ;)

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