# CISRA Puzzle Competition 2007 - Solutions

This is the archive of the 2007 Puzzle Competition. Please visit the current competition site for information about the latest Puzzle Competition.

## A.3 Letter Box

Intuitive Leap: The letters of the "poem" need to be arranged in a box to reveal a secret message.

Steganography is the science of concealing messages in otherwise innocuous data. One way to hide a message in a large body of text is to evenly space the letters of the message throughout the text. This kind of hidden message can be read by arranging the letters in a box, and reading down a column. The title of the puzzle, "Letter Box", is a clue that the letters need to be arranged in a box.

Counting the number of characters in the box gives us these statistics:

```Total length: 540 = 2x2x3x3x3x5
All spaces stripped out: 456 = 2x2x2x3x19
Only letters without punctuation: 403 = 13x31
```

If all spacing and punctuation is ignored, the puzzle has 403 letters. The number 403 has exactly two prime factors: 13 and 31. The text can therefore be arranged in a rectangular box of 13 x 31 letters. If you make a tall skinny rectangle, you get this message along the right-hand edge:

```youchoseTheincorreCtprimefactor
```

Aha! Well, let's try the other prime factor then. Making a short fat box reveals this message on the right-hand edge:

```eraSelastfour
```

So we need to "erase last four". Last four what? Erase the last four letters? If we try that, it leaves us with 399 letters. This number has three prime factors: 3, 7, and 19. Making a box with side-length 3 or 7 yields garbage, but a box of 19 x 21 gives interesting results, again read from the right-hand edge:

```OtHerfactorsproduct
```

All right, so let's try it as a 21 x 19 box:

```youWantthEseCondfruit
```

Hmm. Reading the original text of the puzzle again, we find there are two fruits mentioned: banana and tomato. The "second fruit" is TOMATO. (Yes, tomato is botanically a fruit!)