Question

A competition is being held to select a design for Yancy College's new student union building. Each of six architects - Green, Jackson, Liu, Mertz, Peete, and Valdez - has submitted exactly one design. There are exactly six designs, and they are presented one at a time to the panel of judges, each design being presented exactly once, consistent with the following conditions:

Conditions:

Jackson's design is presented before Liu's.
Mertz's design is presented before Green's and after Peete's.
Valdez's design is presented last.
Which architect's design is presented third?
a) Green
b) Jackson
c) Liu
d) Peete

Answer 1

Based on the constraints, the designs are presented in a specific order with Peete first and Valdez last. Jackson's design must come before Liu's, and Mertz's design must come after Peete's and before Green's. Hence, Green's design is the only possibility to be presented third.

Step-by-step explanation:

To determine which architect's design is presented third at Yancy College's design competition, we must sequence the presentations based on the given conditions. We know Valdez's design is presented last, which makes it the sixth. Mertz's design is presented sometime after Peete's but before Green's. Jackson's design must come before Liu's. So without additional constraints, the sequence we know for sure has Peete before Mertz, Jackson before Liu, and Valdez at the end.

Considering these constraints, we can construct the sequence as follows: Peete (1), Mertz (2), Jackson or Green or Liu (3), Jackson or Green or Liu (4), Liu or Green (5), and Valdez (6). Since Mertz is second and cannot be third, and Valdez is last, we are left with options of Jackson, Green, and Liu for the third position. But based on conditions, Jackson's design cannot be in the third position because Mertz's design is presented after Peete's.

Therefore, laying out the possible order:

1. Peete
2. Mertz
3. Green or Liu
4. the other of Green or Liu
5. Jackson
6. Valdez

Even though exact positions for Green, Liu, and Jackson may be a little uncertain without further information, we can definitely rule out Peete, Mertz (since Peete is first, Mertz is second, and Valdez is last), and Jackson (since Jackson must come before Liu and Liu cannot be in the last two positions because of Green's placement). Therefore, the third presentation must be either Green's or Liu's design. Given the specific choices presented in the question (Green, Jackson, Liu, and Peete), since Jackson and Peete are ruled out and Liu's cannot be third, the only remaining possibility is Green's design as the third presentation.