# Thread: a problem can't understand it

1. ## a problem can't understand it

here is the link of the problem but i can't understand the form of numbers
https://www.spoj.pl/problems/EASYPROB/

2. Originally Posted by mido22
here is the link of the problem but i can't understand the form of numbers
https://www.spoj.pl/problems/EASYPROB/
It's a combination of brain teaser and knowing something about binary.

137 is related to the string "2(2(2)+2+2(0))+2(2+2(0))+2(0)" in that $137=2^{2^2+2^1+2^0}+2^{2^1+2^0}+2^0$. The binary representation of 137 is 10001001. See it?

3. i know about the binary and i understand the

but what is the relation betn. the binary of 137 and this form

4. do u meant that in this binary no.

10001001
the first term (1000) -> the power will be three terms as zeros 2^2+2^1+2^0

and second term (100) -> the power will be two terms as zeros 2^1+2^0

and so on

but here for example
73=2(2(2)+2) +2(2+2(0)) +2(0)
the binary of 73 = 100 100 1
this binary won't help me as i understand

5. Originally Posted by mido22
i know about the binary and i understand the

but what is the relation betn. the binary of 137 and this form
Originally Posted by mido22
do u meant that in this binary no.

10001001
the first term (1000) -> the power will be three terms as zeros 2^2+2^1+2^0

and second term (100) -> the power will be two terms as zeros 2^1+2^0

and so on

but here for example
73=2(2(2)+2) +2(2+2(0)) +2(0)
the binary of 73 = 100 100 1
this binary won't help me as i understand
I am a bit free with my notation in order to write compactly, I think it is legible

$73_{10} = 1001001_2 = 2^6 + 2^3 + 2^0 = 2^{110_2} + 2^{11_2} + 2^0 = 2^{2^2+2^1} + 2^{2^1+2^0} + 2^0$

6. Originally Posted by undefined
I am a bit free with my notation in order to write compactly, I think it is legible

$73_{10} = 1001001_2 = 2^6 + 2^3 + 2^0 = 2^{110_2} + 2^{11_2} + 2^0 = 2^{2^2+2^1} + 2^{2^1+2^0} + 2^0$
i still understanding all except
how can u get that the power of first term is 6 and second is 3 and third is 0 from the binary
if i'mnot silly plz till me what usage of binary here

7. to understand what i want
i understood the image u put and
binary of 6 -> 110 and so on for powers

but how can u get the powers 6,3,0

8. Originally Posted by mido22
i still understanding all except
how can u get that the power of first term is 6 and second is 3 and third is 0 from the binary
if i'mnot silly plz till me what usage of binary here
So in decimal we have for example $12345 = 5\cdot10^0 + 4\cdot10^1 + 3\cdot10^2 + 2\cdot10^3 + 1\cdot10^4$. More symbolically, write an n-digit decimal number as $a_{n-1}a_{n-2}\dots a_1a_0$, then it is equal to $\displaystyle \sum_{k=0}^{n-1} a_k\cdot10^k$.

It is the same in binary, just replace the 10 with 2.

9. i begin to understand u thx very much

10. Originally Posted by mido22
to understand what i want
i understood the image u put and
binary of 6 -> 110 and so on for powers

but how can u get the powers 6,3,0
Originally Posted by mido22
i begin to understand u thx very much
If it's still not clear, see attached image

11. Originally Posted by undefined
If it's still not clear, see attached image
nw it is very very clear thx very much