Unit 16 · Positional Constraint Deduction

Ali's Ingredient Stack — Find the Valid Order

Lesson 1 of 6

Lesson 1 of 6Positional 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.

Best approach: Step 1: Lock the bottom item as given. Step 2: Treat the "directly on top of" pair as a single block — place them together. Step 3: Try arrangements that respect the non-adjacency rules by checking every pair of touching layers. Step 4: Verify the complete stack against all rules. The first valid arrangement you find is the answer — there is exactly one.

Question

Ali stacks five ingredients into a sandwich (each is one layer): bread, chicken, lettuce, cheese, and mayonnaise.

Rules:

  • Bread is the bottom layer.
  • Lettuce must not touch mayonnaise.
  • Cheese must not touch lettuce.
  • Mayonnaise sits directly on top of the chicken.

If Ali follows the rules, which ingredient is on top?

Select an answer to see the explanation.

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