Letter Series and Alphanumeric Series: Finding the Pattern Fast

A letter series is a number series in disguise. The quickest way to find any pattern is to write each letter's position in the alphabet under it, A = 1 to Z = 26, and then look at the gaps between the numbers. Most patterns jump out once you can see the numbers.

To find positions instantly, use the anchor letters E, J, O, T and Y, which sit at 5, 10, 15, 20 and 25. Every other letter is within two places of one of them. The EJOTY trick and reverse positions page covers this in detail, and it is worth learning before you practise series.

When a position goes above 26, subtract 26 to wrap round to the start of the alphabet. When it goes below 1, add 26.

The simplest series add or subtract the same number each time. Check the first two gaps; if they match, test the rest.

If the gaps are not equal, look at the gaps themselves. They often rise by one each time, double, or follow the squares.

Watch for wrap-round near the end of the alphabet. In S, V, Y, ?, the gap is +3, so the next position is 25 + 3 = 28. Subtract 26 to get 2, which is B.

If neither the gaps nor the gaps between gaps make sense, the series may be two separate series woven together. Read only the odd-numbered terms, then only the even-numbered terms. Each half usually has a simple pattern of its own.

A clue that two series are interleaved is a jump back and forth between the two ends of the alphabet, as in this example.

Many questions use groups of two, three or four letters. Look at two things separately: the pattern inside a group, and the step from the first letter of one group to the first letter of the next.

Some groups pair a letter with its opposite in the alphabet, the letter the same distance from the other end. Opposites always add up to 27 in position: A (1) and Z (26), B (2) and Y (25), and so on.

Alphanumeric series combine letters and numbers in each term. Treat them as two series running side by side. Often the number is linked to the letter, for example its position, its position doubled, or its reverse position.

Another common style is the blank-filling series, such as a b _ a b _ a b _, where a short block repeats. Find the length of the repeating block first, then fill each blank from the matching place in the block.

• ✘ Counting positions in your head without writing them down. One slip ruins the pattern.
• ✘ Forgetting to wrap round past Z or before A.
• ✘ Treating an interleaved series as a single series.
• ✘ In letter groups, comparing the wrong letters. Compare first with first, second with second.

The same position arithmetic powers coding-decoding by letter shift. For a wider set of reasoning methods, see the study hub.

What should I try first when a letter series looks random?

Write the position number under every letter and look at the differences. If the differences are not constant, check the alternate terms separately, then check whether the differences themselves form a pattern such as 1, 2, 3 or 2, 4, 8.

What happens when a series runs past Z?

It wraps round to A. Position 27 is A again, 28 is B and so on, so subtract 26 from any position above 26. Backward series wrap from A to Z in the same way.

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