Let a secret three digit number be cba.
If the sum of cab + bac + bca + abc + abc = 2536, what is cba ?

- anonymous

- chestercat

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- anonymous

abc+abc??

- anonymous

it was in the question..

- anonymous

We should let the number be secret.

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## More answers

- experimentX

nice idea

- anonymous

no, open the secret :D

- vishal_kothari

The sum of all six numbers is 222c + 222b + 222a
If u omit cba = (100c + 10b + a), what is left is
N = 122c + 212b + 221a which is what we are given.
Observing 221 = 13*17,
we have N = 5c + 4b mod 13 and N = 3c + 8b mod 17
(u could have used factors of 122 or 212, but 2*61 and
2*2*53 are not nearly so convenient as 13 and 17.)
For N = 2536, we have N mod 13 = 1 and N mod 17 = 3
So u have 1 = 5c + 4b mod 13 and 3 = 3c + 8b mod 17
Since b and c are digits in range 0-9, u can try each value of b for 0 through 9 .
Compute 4 x b and 4 x b mod 13.
Subtract that from 1 to (5c mod 13).
Then find a suitable value for c which satisfies that.
For example 5c = 1 mod 13 -> 5c = 40, c = 8.
compute 3c+8b (mod 17) and find the one which equals 3..
we see it is the row where b = 7 and c = 5.
So we know that the original number was 57a.
To determine a, we take 2536 - 122*5 - 212*7 = 2536 - 610 - 1484 = 442
Dividing by 221, we get a = 2, so the original number was 572.
We can verify that 527+725+752+257+275 = 2536. ..

- experimentX

fun will be gone

- anonymous

hm.. i guess.. this is easier method:
2536 +/-multiple of 99=multiple of 111

- perl

vishal is a fraud , he finds answers online

- perl

here is the banana problem, compare http://www.gottfriedville.net/mathprob/misc-bananas.html

- anonymous

HAHA, lol

- anonymous

copy, paste?

- anonymous

or typed entirely?

- perl

he copied and pasted the whole thing. he is a fraud

- anonymous

ok, lets banish him xD

- perl

whats the challenge in googling?

- anonymous

no challenge, probably the question-poster is making a fun of us :/

- perl

well the question is fine, i dont like people who just post the whole answer. i want to work on it

- perl

well, maybe its not a big deal. ok , forget about it

- perl

better have the answer than not, right?

- experimentX

i agree ...

- perl

ok im angry that he gets a medal for it

- perl

a medal for using google?

- experimentX

it's all right ... medal's just nothing

- anonymous

but i gave him a medal, can i take it back? xD

- anonymous

i became his fan..

- experimentX

still ... i got to see a nice question and answer.

- anonymous

un-fan :D

- perl

hehe

- experimentX

lol ... seriously i don't like the word fan ... i believe we all have equal abilities .. some use and some don't use ... but i think it's fun

- anonymous

but he can do it himself too..

- perl

this one is do-able

- perl

he says, i have all the answers on a file. yeah its called GOOGLE!!!

- anonymous

:D

- anonymous

cab + bac + bca + abc + abc = 2536
100c+10a+b+100c+10a+c+100b+10c+a+2(100a+10b+c) = 2536
213c +221b + 221a =2536
maybe this is good start?

- perl

i still dont understand the gorilla problem

- anonymous

ok, if u would replace last abc by cba, the result would be different, the sum would b divisible by 222
and the difference between them is divisible by 99
then, i guess hit and trial method

- anonymous

the gorilla cant understand how he can solve that too xD

- anonymous

213c +(a+b)221 = 2536
but this gives more then one solution if 221 is more than once

- anonymous

and it does

- anonymous

cab + bac + bca + abc + abc = 2536
100c+10a+b+100c+10a+c+100b+10c+a+2(100a+10b+c) = 2536
213c +221b + 221a =2536
maybe i made a mistake here somehere...

- anonymous

No :/ this isn't right

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