mathschallenge.net

Problem

Sitting in your comfy chair one evening and reading a good book, you notice something white behind the ventilation grill next to the fireplace. Carefully removing the grill you discover a white envelope containing a diskette and a piece of paper. Excitedly you check-out the disk, which contains a program. When you run the program you are greeted with the cryptic message: X hits the spot, but what does X represent? A small text box on the screen seems to be awaiting an answer. A little disappointed and confused you unfold the piece of paper and read the following:

T R O O C H X X I A O O
O P X O N F O O C T X O
H O O X L E X O I A O X
E H O O W T O X E U X O

What does X represent?

Solution

A subtle clue was provided in the location of the white envelope; as it was behind a grill, the code makes us of a "grille" principle.

The first stage is to realise that every 3rd and 4th character is either an O or an X. Begin by writing the encrypted message in blocks of four:

T R O O
C H X X
I A O O
O P X O
N F O O
C T X O
H O O X
L E X O
I A O X
E H O O
W T O X
E U X O

Then to decrypt we use the 3rd and 4th characters on each line as a template/grille. By placing the 3rd and 4th characters on top of the 1st and 2nd characters, we ignore any characters that are not marked by an X:

    O O
C H X X
    O O
O   X O
    O O
C   X O
  O O X
L   X O
  A O X
    O O
  T O X
E   X O

Hence the X represents CHOCOLATE – which certainly hits the spot! ;o)