This solution comes from Andrei from School No. 205,
Bucharest, Romania.
To solve this problem I followed the following steps:
- associating to the letters of the alphabet numbers between 0
and 25, I transformed the coded message into a set of pairs of
numbers
- I solved the system of
equations for
in terms of
.
- I used the same association as in the first step, and I
transformed the set of numbers
into letters, and
I found the message.
The association is:
| | a | b | c | d | e | f | g | h | i | j | k | l | m | n | o | p | q | r | s | t | u | v | w | x | y | z |
| | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |
For each pair of numbers
I have to solve the
system to determine
|
|
I start from the last equation:
To determine 1/5 (mod 26), I first constructed the table of
multiplication for 5 (mod 26) to see where I obtain 1. As 21
multiplied by 5 gives 1 (mod 26) it follows that 1/5 (mod 26) is
21. This means:
and for
I obtained successively
|
|
that is
Now, the sequence of numbers
is transformed by equations (3) and (4) into the sequence
| C |
|
|
|
| P |
| dj | 3 | 9 | 8 | 7 | ih |
| lb | 11 | 1 | 0 | 21 | av |
| rn | 17 | 13 | 4 | 13 | en |
| qm | 16 | 12 | 14 | 18 | os |
| bu | 1 | 20 | 15 | 4 | pe |
| ao | 0 | 14 | 2 | 8 | ci |
| hd | 7 | 3 | 0 | 11 | al |
| eo | 4 | 14 | 6 | 8 | gi |
| kr | 10 | 17 | 5 | 19 | ft |
| ia | 8 | 0 | 8 | 0 | ia |
| cs | 2 | 18 | 12 | 14 | mo |
| ud | 20 | 3 | 13 | 11 | nl |
| rx | 17 | 23 | 24 | 15 | yp |
| cm | 2 | 12 | 0 | 18 | as |
| qo | 16 | 14 | 18 | 8 | si |
| bn | 1 | 13 | 14 | 13 | on |
| fr | 5 | 17 | 0 | 19 | at |
| ld | 11 | 3 | 4 | 11 | el |
| ek | 4 | 10 | 24 | 2 | yc |
| th | 19 | 7 | 20 | 17 | ur |
| ys | 24 | 18 | 8 | 14 | io |
| wm | 22 | 12 | 20 | 18 | us |
The message could be read as the quotation from Enstein talking about himself as a mathematician:
'I have no special gift. I am only passionately
curious'.