Polynomial Cipher

Computer Science Level 2

You've just received a message from Alice! Before you can read it though, you'll have to decipher it. The encrypted message you received was "13417108788227" .

You know Alice encrypted it using the following method:

  1. Convert each letter into a two-digit number corresponding to its position in the alphabet. 'A' turns into "01", 'B' into "02", and 'Z' into "26". The word "CAR" becomes "030118".

  2. Pass the converted words through the encryption function E ( x ) = 2 x 4 + 3 x 3 + x 2 + 4 x + 1. E(x) = 2x^4 + 3x^3 +x^2 + 4x + 1. For example, "CAR" becomes E(30118).

Let M be Alice's original unencrypted message. What is the alphabetic position of the first letter of M ? ('A' is in position 1, 'B' is in position 2, and 'Z' is in 26.)


The answer is 16.

View wiki
Maryann Vellanikaran by Maryann Vellanikaran , 36, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Discussions for this problem are now closed

Nimisha Soni
May 14, 2014

Original message was PI i.e 1609

2 x 4 + 3 x 3 + x 2 + 4 x + 1 = 13417108788227 2 x 4 + 3 x 3 + x 2 + 4 x − 13417108788226 = 0 ( x − 1609 ) ( 2 x 3 + 3221 x 2 + 5182590 x + 8338787314 ) = 0 ( x − 1609 ) = 0 o r ( 2 x 3 + 3221 x 2 + 5182590 x + 8338787314 ) = 0 x − 1609 = 0 ⇒ x = 1609 [ P = 16 , I = 09 ] 2{ x }^{ 4 }+3{ x }^{ 3 }+{ x }^{ 2 }+4x+1=13417108788227\\ 2{ x }^{ 4 }+3{ x }^{ 3 }+{ x }^{ 2 }+4x-13417108788226=0\\ (x-1609)(2{ x }^{ 3 }+3221{ x }^{ 2 }+5182590x+8338787314)=0\\ (x-1609)=0\quad or\quad (2{ x }^{ 3 }+3221{ x }^{ 2 }+5182590x+8338787314)=0\\ x-1609=0\quad \quad \Rightarrow \quad \quad x=1609\quad \quad [P=16,I=09]

17 Helpful 1 Interesting 2 Brilliant 8 Confused
Aaaaa Bbbbb
May 10, 2014

Call this number A B X 1 X 2 . . . X 2 n = A B + X ABX_1X_2...X_2n=AB+X 2 × ( A B × 1 0 2 n + X ) 4 < 13417108788227 ⇒ n = 1 2 \times (AB\times10^{2n}+X)^4 < 13417108788227 \Rightarrow n=1 2 × A B C D 4 + 3 × A B C D 3 + A B C D 2 + 4 × A B C D + 1 = 13417108788227 ⇒ A B = 16 2 \times ABCD^4+3 \times ABCD^3+ABCD^2+4 \times ABCD+1=13417108788227 \Rightarrow AB=\boxed{16}

3 Helpful 0 Interesting 0 Brilliant 6 Confused

An interesting name you have there :D

Yuxuan Seah - 7 years, 1 month ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...