Concepts · Letter series and coding

Wrapping past Z

The alphabet does not stop at Z. Neither should you.

Kabir is halfway through a mock test when he meets this:

U, X, A, D, ?

U to X is three steps. Fine. X to A is… twenty-three steps back? He checks it twice, decides it is a misprint, writes a question mark in the margin and moves on.

The train ticket

After the test, Riya asks when his train leaves. Kabir looks at his ticket.

“Fifteen thirty. Three thirty, I mean. I took away twelve.”

He hears himself say it and stops. He took away twelve because a clock has no fifteenth hour: after 12 it goes round to 1. He pulls the question paper out of his bag. The alphabet has no 27th letter either. After Z, it must go round to A.

The rule

After Z comes A. In positions: if you go past 26, take away 26. If you go back past 1, add 26.

Kabir’s question, again

1. U is 21 and X is 24: a step of 3.
2. 24 + 3 = 27. That is past 26, so take away 26: 1, which is A.
3. A to D is 3. D to G is 3. The answer is G.

Nothing was broken. The series just walked round the corner.

Finding positions fast: E is 5, J 10, O 15, T 20, Y 25. That is its own concept, Letter positions.

Going backwards

Kabir tries it the other way. Three letters before B? B is 2, and 2 − 3 = −1. That is below 1, so add 26: 25, which is Y.

Why it helps in the paper

Stop at Z and the question looks broken, and the only moves left are a guess or giving up. Count round the corner and it is an ordinary question. The wrap turns up in letter series, in letter-and-number series such as W3, Z6, C9, and in codes that move every letter forward.

Try three

Next mock

Two weeks later, Kabir meets Y, B, E, ? He does not reach for the margin. Y is 25; 25 + 3 = 28, take away 26: 2, which is B. So the step is 3, and E is 5: 5 + 3 = 8. He writes H.