Letter-number-symbol series, position-counting, and machine input-output (shifting, arranging, coding) reasoning, with worked examples and practice
Two pattern-tracking reasoning types. Alphanumeric series mixes letters, numbers, and symbols in one string and asks position-based questions. Input-output (the "machine" type) gives a rule that rearranges a line of words or numbers step by step and asks for an intermediate or final step. Both reward careful counting and a fixed reference, not cleverness. They pair well with the coding and series work in verbal reasoning.
| Letter | Forward position | Backward position |
|---|---|---|
| A | 1 | 26 |
| E | 5 | 22 |
| J | 10 | 17 |
| M | 13 | 14 |
| N | 14 | 13 |
| Z | 26 | 1 |
Two anchors do most of the work: the EJOTY rule (E is 5, J is 10, O is 15, T is 20, Y is 25, each five apart) and the opposite-letter sum rule (forward position plus backward position = 27, because there are 26 letters). So the letter opposite to the kth from the start is the kth from the end.
A typical string is a fixed sequence of letters, digits, and symbols, for example:
5 P @ K 3 # T 9 B % 7 M
Read the whole string once, then answer position questions by counting from the stated end.
| Question type | How to handle it |
|---|---|
| Nth from the left or right | count directly; for "Nth from right", start at the right end |
| Element between two markers | locate both markers, read what lies between |
| How many digits are immediately followed by a symbol | scan adjacent pairs left to right |
| Nth to the left of the Mth from the right | first fix the Mth from the right, then step N places left |
The reliable trick for "Nth to the left of the Mth from the right" is: convert everything to a single direction. The position from the left of the Mth-from-right is (total length minus M + 1), then move left by N.
A word-and-number arrangement machine takes an input line and, at each step, applies one rule to one element, building toward a sorted or coded output. Common rules:
| Rule family | What it does |
|---|---|
| Shifting | moves one element (often the largest number or the alphabetically last word) to one end each step |
| Arranging | sorts words alphabetically or numbers in ascending or descending order, one per step |
| Alternating | applies word-rule and number-rule on alternate ends |
| Coding | replaces an element with a coded form (reversed, +1 letter, squared number) each step |
The number of steps usually equals the number of elements that need to move, minus one. To crack such a set, compare consecutive given steps to infer the single rule applied each time, then run it forward.
For Examples 1 to 4, use the string:
7 R $ 2 K M 9 # P 4 @ B 8 W
(positions 1 to 14 from the left).
What is the 4th element from the right?
From the right the order is W(1), 8(2), B(3), @(4). The 4th from the right is @.
Which element lies exactly midway between K and P?
K is at position 5, P at position 9. Midway is position 7, which is 9.
How many digits are immediately followed by a letter?
Scan: 7 then R (yes), 2 then K (yes), 9 then # (no, symbol), 4 then @ (no), 8 then W (yes). Three digits are immediately followed by a letter.
Which element is 3rd to the left of the 6th from the right?
6th from the right: from the right W(1), 8(2), B(3), @(4), 4(5), P(6), so the 6th from the right is P at left-position 9. Three places to the left of position 9 is position 6, which is M.
What is the 18th letter of the alphabet?
T is the 20th, so step back two: 19th is S, 18th is R.
Which letter is opposite to F (that is, F is the kth from the start, find the kth from the end)?
F is the 6th letter. Forward plus backward = 27, so its opposite is the (27 minus 6) = 21st, which is U.
Input: 35 12 48 27 6. Step 1: 6 35 12 48 27. Step 2: 6 12 35 48 27. What is step 3?
The rule moves the smallest remaining number to the front each step. After 6 and 12, the next smallest is 27. Step 3: 6 12 27 35 48.
For questions 1 to 5, use the string:
Q 4 % T 8 D 1 @ N 6 K # 3 H
(positions 1 to 14 from the left).
8.#.8.@.