Hello everyone,
I was trying to solve 43C - Счастливые билеты , 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 ,
try this Khan Academy
Thank you :D
I learned that in primary school, so it does seem elementary.
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.
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