Concepts · Coding and decoding

Opposite letters

A code that looks scrambled can be the alphabet folded in half.

Kabir meets this in a mock test:

If GOLD is coded as TLOW, how is HOT coded?

G to T is thirteen steps forward. O to L is three back. L to O is three forward. D to W is nineteen forward. No one step fits all four. He calls it a scramble and guesses.

The ludo die

That evening he is playing ludo with Riya. He rolls a 2 and, without looking, says, “Five underneath.”

“You can’t even see it.”
“Don’t need to. Opposite faces make seven. One and six, two and five, three and four.”

One warning. This is true of the ludo die at home. Dice questions in exams can use dice where it is not, so never assume it there.

Opposite faces, every pair making the same number. Kabir stops with the die in his hand. He takes the mock paper out of his bag and adds the positions of each letter and its code: G and T, 7 + 20 = 27. O and L, 15 + 12 = 27. L and O, 27 again. D and W, 4 + 23 = 27.

The alphabet has opposites too. Fold it in half and A lands on Z, B on Y, C on X, all the way to M on N. And because A is 1 and Z is 26, every pair makes the same number: 27.

The rule

Each letter has an opposite at the other end of the alphabet, and the two positions add to 27. So the opposite of a letter is 27 minus its position.

Kabir’s question, again

1. Every letter of GOLD has been replaced by its opposite: each pair of positions adds to 27.
2. H is 8: 27 − 8 = 19, which is S. O is 15: 27 − 15 = 12, L. T is 20: 27 − 20 = 7, G.
3. HOT is coded as SLG.

Positions come fastest from the anchors E 5, J 10, O 15, T 20, Y 25: Letter positions.

Decoding is the same move

Opposites go both ways: the opposite of S is H. So to decode SLG you do exactly what you did to code HOT. And no letter is its own opposite. The fold falls between M and N.

Why it helps in the paper

It looks random, and that is what makes it hard: checking only “how many steps forward?” gives a different answer for every letter. One line settles it: add the positions of each letter and its code. If every pair makes 27, you have found the rule.

It has a name: Atbash

It began with the Hebrew alphabet, where the first letter, aleph, swaps with the last, tav, and the second, bet, with the second-last, shin. Put those four together, A-T-B-Sh, and you have its name. The Book of Jeremiah is traditionally read as using it: “Sheshach” for Babel. The code is far older than any exam.

Try three

Next mock

Two weeks later: “In the same code, what does WLT stand for?” Kabir does not count steps. W is 23, and 27 − 23 = 4: D. L is 12, and 27 − 12 = 15: O. T is 20, and 27 − 20 = 7: G. He reads it out: “DOG!” Riya does not look up from her book. “Woof.”