Letter sequences and codes

Notes

Key idea: letters are just numbers in disguise. A = 1, B = 2, and so on up to Z = 26. Turn the letters into numbers, spot the pattern, then turn the answer back into a letter.

The alphabet in numbers

Tip: write the alphabet with numbers underneath at the start of the test. It takes 20 seconds and saves mistakes.

Types of pattern

1. Constant step. The same jump each time. A, C, E, G: always +2.
2. Growing steps. The jump gets bigger. B, D, G, K: the steps are +2, +3, +4, so the next step is +5 and the next letter is P.
3. Backwards. Z, X, V, T: always −2.
4. Alternating steps. The jump alternates. A, C, D, F, G: +2, +1, +2, +1, so next is I.
5. Two sequences mixed together. Take every other letter. A, Z, C, X, E, V: the odd positions go A, C, E (+2) and the even positions go Z, X, V (−2).

Wrap-around

After Z comes A again. X, Z, B, D: X (24), Z (26), B (2, which is 28 − 26), D (4).

Letter codes

A shift code moves every letter the same number of places. With a shift of +1, CAT becomes DBU.

To decode, shift the opposite way. If a +3 code gives KHOOR, shift each letter back 3: K→H, H→E, O→L, O→L, R→O. The word is HELLO.

A number code writes each letter as its position. With A = 1, the word CAT is 3, 1, 20.

Common mistakes

• Counting the letters you pass instead of the step. From A to C is a step of 2 (A, B, C), not 3.
• Forgetting that the alphabet wraps round after Z.
• Missing a two-sequence pattern: if the steps look random, look at every other letter.