Here is another brilliant solution from Andrei from School No. 205, Bucharest, Romania

I have to find the secret message

20 14 19 23 11 13 20 21 4 5 11 23 18 6 19 14 19 4 13 21 24 16 19 20 14 21 4 7 17 24 11 1 20 20 14 19 15 11 6 16 12 21 13 20 14 17 20 21 20 21 13 5 11 23 18 6 19 14 19 4 13 21 24 16 19

which has been coded by using the equation:

C=7P + 17 mod 26

where C is the cipher value of the corresponding P and P represents the letters of the alphabet taking a=0, b=1, c=2, ... to z=25.

Solving this equation for P gives

P= 1 7 C - 17 7 mod 26.

Using the reverse of the multiplication table mod 26, I found:

P = 15C - 21 = 15 C + 5 mod 26     (1)

Performing the operations in equation (1) using the properties of arithmetic operations mod 26, I found the following sequence of numbers 19, 7, 4, 12, 14, 18, 19, 8, 13, 2, 14, 12, 15, 17, 4, 7, 4, 13, 18, 8, 1, 11, 4, 19, 7, 8, 13, 6, 26, 1, 14, 20, 19,19, 7, 4, 22, 14, 17, 11, 3, 8, 18, 19, 7, 26, 19, 26, 18, 2, 14, 12, 15, 17, 4, 7, 4, 13, 18, 8, 1, 11, 4. These, transformed into words, produced the following message:

"The most incomprehensible thing about the world is that it is comprehensible".