Logic Games: Sequencing and Ordering Games Flashcards

Seven runners — F, G, H, I, J, K, L — finish a race in distinct positions 1–7. G finishes immediately before H. J finishes after K but before I. F finishes last. Which of the following is a complete and accurate list of runners who CANNOT finish third?

Answer: F, G, I

F is fixed at 7th; G must be followed immediately by H so G cannot be 7th or 6th unless space allows, but G and H must have H directly after G; I must come after J and after K, requiring at least two runners before it, so I cannot be 1st, 2nd, or (given constraints) 3rd.

In a strict sequencing game, six tasks — P, Q, R, S, T, U — must be completed in order. R is completed before S. T is completed before P. U is completed immediately after Q. If S is completed fifth, which of the following must be true?

Answer: R is completed third or earlier.

Since S is fifth, R must be in positions 1–4; with P, Q, T, U also needing placement, R must be third or earlier to accommodate all constraints.

Five presentations — A, B, C, D, E — are scheduled one per slot, slots 1–5. A is scheduled before C. D is scheduled before B. E is not scheduled first or last. How many different complete orderings are possible?

Answer: 12

Applying A<C, D<B, and E in positions 2–4 yields exactly 12 valid orderings when systematically enumerated.

In a sequencing game, eight books are shelved left to right. Book M is shelved somewhere to the left of book N. Book O is shelved immediately to the right of book P. If N is shelved in position 6, which of the following CANNOT be true?

Answer: P is shelved in position 8.

O is immediately to the right of P, so P cannot be in position 8 because there is no position 9 for O.

A strict linear ordering has conditions: X comes before Y; Y comes before Z; W comes before X. If exactly one person stands between W and Z, which of the following must be true?

Answer: X is between W and Z.

The chain W<X<Y<Z spans at least 4 positions; if exactly one person is between W and Z, then W, X, and Z occupy three consecutive slots with X as the sole person between W and Z, and Y must equal X — impossible — so X must be the one between W and Z, making Y=Z which is also impossible unless we interpret the chain as W _ Z with X the single person between them, confirming X is between W and Z.

In a sequencing game, six athletes finish in positions 1–6. Athlete 1 (first place) scored highest. Constraints: Q finishes before R; S finishes before Q; T finishes last. If R finishes in position 3, which position must S occupy?

Answer: Position 1 or 2

S<Q<R and R is in position 3, so Q must be in position 2, and S must be in position 1 or 2 — but Q is in 2, so S must be in position 1.

Seven students — 1 through 7 — line up. Student A is not first. Student B is immediately before student C. Student D is somewhere after student E. If student B is fourth, which of the following could be a complete and accurate ordering of students E, D?

Answer: E in position 6, D in position 7

E must come before D; E in 6 and D in 7 satisfies E<D, and with B in 4 and C in 5, there are no additional conflicts.