OmarKhaled_'s blog

Mathematical facts

By OmarKhaled_, history, 9 years ago, In English

Hello everyone,

I was trying to solve 43C - Lucky Tickets , I couldn't come up with a correct solution in the time limit so I read the editorial , the writer stated " We all know that the remainder of a number when divided by 3 is equal to the remainder of sum of its digits when divided by three.", apparently that was a key fact for solving the problem but I lacked this certain knowledge.The way he wrote it gave me an impression that it is an elementary piece of information that I should surely know. I tried searching it, I didn't come up with anything about this fact or a proof. Am I supposed to deduce a fact like this during solving the problem or is it a well-known fact and I lack enough knowledge ? It will be great if you could direct me to a source where I could learn useful similar facts which could be a key for solving coming problems.

Thank you ,

  • Vote: I like it
  • +13
  • Vote: I do not like it

»
9 years ago, # |
  Vote: I like it +8 Vote: I do not like it

try this Khan Academy

→ Reply
»
9 years ago, # |
  Vote: I like it +35 Vote: I do not like it

I learned that in primary school, so it does seem elementary.

→ Reply
  • »
    »
    9 years ago, # ^ |
    ← Rev. 3   Vote: I like it +9 Vote: I do not like it

    Yeah, indeed, absolutely everybody (at least in Poland) is taught in primary school that , fact you mentioned is just a slightly stronger statement that originates from proof of it. Of course proving this will be probably beyond math abilities of 99% people ending high school, but also of course, measuring math abilities of CF folks with respect to a typical human is not very meaningful :P.

    EDIT: Btw I just realized that this 'generalization' is straightforward conclusion from that fact I mentioned even when treated as a blackbox (we can apply that to some number from interval [x-2, x+2]), we do not have to delve into proof, so we can say that average 10 year old Pole should know this : D.

    → Reply
    • »
      »
      »
      9 years ago, # ^ |
        Vote: I like it +13 Vote: I do not like it

      So it's my bad. I could have missed my class that day , or probably folks here who teach us unlike yours and Xellos decided that this was unnecessary to be taught to a 10 year old.Anyway, it was a nice chance to come up with what I missed , the link provided by 0xA28 was very good.THANKS! :D

      → Reply