Unit 16 · Positional Constraint Deduction
Sam's Five Items — Find the Valid Stack
Lesson 1 of 2
Stacking puzzles start with anchors: fix the bottom layer, lock the “directly on top of” pair as one block, then add layers while checking “must not touch”.
Vertical stack items appear in the medium band of Selective TS — students who place the locked pair first avoid trying every permutation.
The examiner checks whether you can build the only valid bottom-to-top order using a fixed base, one consecutive pair, and non-adjacency bans.
Five layers from bottom to top. One item is fixed at the base. One pair must be consecutive. Some pairs cannot be adjacent. You name the top layer.
Best approach: Layer 1 = given bottom. Treat [turkey][cream cheese] as a block. Slot remaining items between rules; any touch between banned neighbours eliminates that try.
Question
Sam stacks five items in a lunchbox (each is one layer, from bottom to top): wrap, turkey, spinach, tomato, and cream cheese.
Rules:
- Wrap is the bottom layer.
- Tomato must not touch cream cheese.
- Spinach must not touch tomato.
- Cream cheese sits directly on top of the turkey.
Which item is on top?
Select an answer to see the explanation.
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