UCAT logical puzzles: ordering questions
Place anything fixed first: an end, a slot number. Then glue pairs that move together, like B immediately before D. Then test the options against the clues instead of building every order. Try two below.
Folders A, B, C, D occupy consecutive numbered shelf positions from left to right, one folder per position. There is exactly one position between A and C. A is immediately before B. Which of the following orders is possible?
Worked answers
1. Folders A, B, C, D occupy consecutive numbered shelf positions from left to right, one folder per position. There is exactly one position between A and C. A is immediately before B. Which of the following orders is possible?
Answer: A: D, A, B, C
- In D, A, B, C, there is exactly one position between A and C.
- In D, A, B, C, A is immediately before B.
2. Presentations A, B, C, D, E, F occupy consecutive numbered slots, one presentation per slot. D is at neither end. A is immediately before B. D is immediately before E. B is before F. F is before E. A is before C. B is immediately before F. Which of the following orders is possible?
Answer: D: A, B, F, C, D, E
- In A, B, F, C, D, E, D is at neither end.
- In A, B, F, C, D, E, A is immediately before B.
- In A, B, F, C, D, E, D is immediately before E.
- In A, B, F, C, D, E, B is before F.
- In A, B, F, C, D, E, F is before E.
- In A, B, F, C, D, E, A is before C.
- In A, B, F, C, D, E, B is immediately before F.
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Clues by strength
| Clue | How strong | Use it |
|---|---|---|
| X is in slot 3 | Fixed | Place it first |
| X is immediately before Y | A block | Treat XY as one item |
| Exactly one between X and Y | A gap | List the few places it fits |
| X is before Y | Weak | Use last, to rule options out |
Must, could, cannot
"Must be true" needs every valid order. "Could be true" needs just one. One counterexample is enough to rule out "must".
Keep going
Practise orders on a board: UCAT DM order lab
Every Decision Making type: DM question types and methods