Coding-Decoding: Letter Shifts, Reverse Alphabet and Number Codes

Most coding-decoding questions replace each letter of a word with another letter, or with a number, according to a fixed rule. The rule is almost always about a letter's position in the alphabet: A = 1, B = 2, up to Z = 26. If you can turn letters into numbers quickly, you can see the rule quickly.

The standard memory aid is EJOTY: E = 5, J = 10, O = 15, T = 20, Y = 25. To find R, count two back from T (20): R = 18. Every letter is within two steps of an anchor.

The simplest rule moves every letter the same number of places. Compare the first letter of the word with the first letter of its code, find the gap, and check that the same gap works for the second letter before applying it to the new word.

Shifts wrap round the end of the alphabet: after Z comes A again. Treat the alphabet as a circle of 26 letters.

When a fixed shift does not fit, write down the shift for each letter. A common pattern is +1, +2, +3, +4, where each letter moves by its own position in the word.

Other patterns you may meet are alternating shifts (+1, −1, +1, −1), shifts that fall (+4, +3, +2, +1), or a word written backwards and then shifted.

In this code each letter is replaced by the letter the same distance from the other end: A↔Z, B↔Y, C↔X and so on. The two positions always add up to 27, so the opposite of a letter at position n is at position 27 − n.

A useful set of pairs to remember is the word pairs that are already opposite letters: A–Z, B–Y, C–X, D–W, E–V, F–U, G–T, H–S, I–R, J–Q, K–P, L–O, M–N. If you forget a pair, use the rule that the two positions add up to 27.

A different style gives several coded sentences, such as "sky is blue" written as "ka pa ta" and "blue is deep" written as "ta ra ka", and asks for the code of one word. Here letter positions do not help; compare sentences instead. A word that appears in two sentences must have the code that appears in both. In this example, "is" and "blue" are shared, and so are "ka" and "ta", so "sky" must be "pa" and "deep" must be "ra". Work out the single-word differences first, then use them to separate the shared codes, and say "cannot be determined" if two codes are always seen together.

When a word is coded as a single number, try the sum of letter positions first, then the product, then the sum of opposite positions.

Sometimes each letter becomes its own number and the numbers are written side by side, so CAT is 3120. Look at the length of the code: a long string of digits usually means letter-by-letter numbers, while a short number usually means a sum.

• ✘ Testing the rule on only one letter. Confirm it on at least two before using it.
• ✘ Forgetting to wrap from Z back to A.
• ✘ Mixing up forward and backward shifts. Check the direction on the first letter.
• ✘ Assuming a fixed shift when repeated letters are coded differently.

More reasoning methods: direction sense, calendars and clock angles.

How do I find letter positions quickly?

Memorise EJOTY: E is 5, J is 10, O is 15, T is 20 and Y is 25. Every letter is at most two places from one of these anchors, so you can count to any position in one or two steps instead of counting from A.

What if the shift pattern is not the same for every letter?

Write the change for each letter as a number, such as +1, +2, +3, or +2, −2, +2. The numbers usually form a simple pattern, increasing by one, alternating in sign, or matching the letter's place in the word.

All problems and solutions on this page are original. No outside facts are relied on; every numeric answer is recomputed by software before publishing.