Positional Constraint Deduction

Positional Constraint Deduction questions ask you to place items into specific positions — a stack, a row, or a grid — while satisfying a set of hard rules about what can and cannot be adjacent. Let's start with the most teachable one-dimensional variant: a vertical stacking puzzle. The secret is that one constraint always acts as the anchor — lock that in first, and the rest follows.

Stacking and sequencing problems with "directly on top of" and "must not touch" constraints appear consistently in the medium difficulty band of OC TS. Students who identify the anchor constraint early solve them in seconds; students who try every permutation waste time and risk errors.

The examiner is checking whether you can identify the most specific constraint — the "X directly on top of Y" clue that creates a locked consecutive pair — and use it as the starting point to build the arrangement, then verify each adjacency constraint as layers are added.

Five items must be stacked from bottom to top. One item is anchored at the bottom. One pair must be consecutive (X directly on top of Y). Additional rules prohibit certain adjacent pairs. You must find which item sits at the very top in the only valid arrangement.

Six towns, five compass clues, one diagram. This question looks intimidating because of the number of towns and relationships, but the secret is to place the towns one clue at a time rather than trying to visualise all of them at once. The moment you anchor D at the bottom and build upward and outward, the map assembles itself in about 30 seconds.

Text-based compass direction mapping appears occasionally in OC TS, usually at the medium difficulty level. The question always gives exactly as many clues as needed to produce one unambiguous map. Students who draw as they read score reliably; students who try to hold the whole map in their head make errors on the east–west placements.

The examiner is checking whether you can translate each compass direction clue into a grid position, build a complete map by applying clues sequentially, and then correctly identify a compound direction (e.g. "northwest") from that map. The trap is confusing "due north" with "northwest" — the two are different.

Five or six towns are described with cardinal and ordinal direction relationships (north, northeast, west, etc.). After placing all towns on a mental or drawn grid, you identify the direction or relative position of a specific town from another. Compound directions (northwest, southeast, etc.) are tested because students often place B "due north" and then wrongly label it "northwest."

A word game assigns a whole-number value (≥ 1) to each letter. You are given four example words and their scores. From those, can you work out the value of each letter and calculate the score for THAW? This is a classic substitution puzzle: each equation gives you information, and combining them lets you solve for every unknown.

Letter-value or symbol-value puzzles appear regularly in OC TS. They typically give 3–5 example totals and ask for the total of a new combination. The key skills are: recognising shared letters between equations (to eliminate variables), and remembering the "whole number ≥ 1" constraint when there are multiple possible solutions for a pair.

The examiner is testing whether students can set up and solve a simple system of equations using substitution. The '≥ 1' constraint is deliberate — it is the only way to pin down the unique value of O (and therefore T). Students who assume O = 2 will get T = 0, violating the constraint, and end up with a wrong answer for THAW.

Four words and their scores are given. The words share letters, so each new equation adds information. Identify which pair of words differs by exactly one letter (TOO vs TWO: swap one O for W) to isolate a relationship between two letters. Then use the constraint that each value is a whole number ≥ 1 to pin down exact values. Finally substitute into the target word.

Now for a 2D positional puzzle — four seats in a car arranged in a 2×2 grid. This is harder than a linear stack because constraints operate in two directions: "next to" means side by side in the same row, while "directly behind" means same column in a different row. Getting those directions right is the difference between a quick solve and a wrong answer.

Car seating, table seating, and rectangular grid placement problems appear regularly in the difficult range of OC TS. The key skill is correctly translating spatial language ("next to", "directly behind", "not in the back") into grid positions before placing anyone.

The examiner is testing whether you can map spatial language onto a 2D grid correctly, apply an either-or constraint to eliminate one option through forced placement of other people, and find the unique valid seating arrangement.

Four or six people must be placed into a 2×2 or larger grid of named seats (front-left, front-right, back-left, back-right). Each person has one or two constraints — a specific allowed or forbidden seat, a side-by-side restriction, or a same-column rule. You identify who sits where and answer a specific placement question.

Train table seating combines two types of constraint at once: which direction a person is facing (forward or backward) AND which type of seat they have (window or aisle). This question adds a third spatial relationship — "diagonally opposite" — that students sometimes confuse with "directly opposite." Getting those three terms right is the whole game.

Train and table seating puzzles appear in the difficult range of OC TS and are among the most richly constrained positional problems. They are especially valued by examiners because students who rush and confuse "diagonal" with "direct" pick wrong answers confidently. Methodical case-testing is the only reliable approach.

The examiner is checking whether you can (1) correctly interpret "diagonally opposite" vs "directly opposite" vs "next to" in a 2×2 grid, (2) systematically test all possible placements and eliminate those that break any constraint, and (3) identify which conclusion is true in every valid arrangement rather than just one.

Four people are placed in a 2×2 train table (forward/backward × window/aisle). You are given three constraints — a diagonal relationship, a direction for one person, and an adjacency rule. Two valid arrangements usually survive the elimination. The correct answer is the statement that is true in both.

Five chests in a row, five clues, and only one chest with the key to freedom. This is the richest positional constraint puzzle in this unit — it combines "far right" anchoring, distance-based placement, "left of" ordering, and adjacency exclusions. The secret is to start with the clue that gives an absolute position (black is at far right), then chain outward to place each remaining chest.

Five-item row placement puzzles appear in OC TS at the difficult level and are among the most time-intensive questions in the paper. They reward students with a systematic, step-by-step placement approach. Students who try to test all permutations without anchoring first run out of time and make errors.

The examiner is checking whether you can anchor the arrangement from the one absolute clue (Black = position 5), derive the next placement from a distance clue (White = 3), then use exclusion clues to force every remaining colour into its unique position, and finally use the two key-location clues in sequence to identify which colour holds the key.

Five coloured items must be placed in a numbered row. One clue gives an absolute position ("at the far right"). Other clues give distances ("2 places away"), orderings ("to the left of"), and adjacency restrictions ("not next to"). You chain all clues to build the unique valid arrangement, then use the final clue to identify the target item.