Thinking Skills
Leo, Maya, Ned, and Olivia are the four finalists in the school Talent Quest. They will perform one after the…
Question 1 · Multiple choice
Question
Leo, Maya, Ned, and Olivia are the four finalists in the school Talent Quest. They will perform one after the other. Each student gets exactly one performance slot: 1st, 2nd, 3rd, or 4th.
| Clues: |
|---|
| - Leo will perform either 1st or 4th. |
| - If Leo performs 1st, then Maya will perform 3rd. |
| - If Maya performs 3rd, then Ned will perform 2nd. |
| - Olivia has to leave early for a dentist appointment, so she absolutely cannot perform 4th. |
Options
Which one of the following statements must be true?
- A.Maya performs 2nd.
- B.Leo performs 4th.
- C.Ned performs 1st.
- D.Olivia performs 3rd.
Correct answer
Explanation
For Ordering puzzles, do not draw a grid with ticks and crosses. Instead, draw a simple timeline with blank spaces.
Step 1: Draw the Timeline & Find the Anchor
Draw four blank slots. Look for the absolute rule. The last rule tells us Olivia cannot be 4th. We write that beneath the 4th slot so we don't forget it.
[ 1st ] [ 2nd ] [ 3rd ] [ 4th ]
___ ___ ___ ___
(NOT Olivia)
Step 2: The "What-If" Test (Pushing the Domino)
Look at the first rule: "Leo will perform either 1st or 4th." We don't know which one, so we must run a What-If Test. We look at the "If" rules below it and see they are triggered by Leo being 1st.
Assumption: What if we put Leo in the 1st slot?
Let's watch the dominoes fall:
- Domino 1: If Leo is 1st, the rules say Maya must be 3rd.
- Domino 2: If Maya is 3rd, the rules say Ned must be 2nd.
Let's write this out on our test timeline:
[ 1st ] [ 2nd ] [ 3rd ] [ 4th ]
LEO NED MAYA ___
(NOT Olivia)
Step 3: The CRASH! 💥
Look at the 4th slot on our Test Timeline! Because our chain reaction filled up the 1st, 2nd, and 3rd slots, there is only one slot left in the entire show. That means Olivia is forced to take the 4th slot.
But wait! Our Anchor Fact explicitly says Olivia cannot perform 4th!
We have forced Olivia into an impossible position. CRASH!
Step 4: The Final Deduction
Because our assumption caused a timeline crash, our assumption was wrong.
- Leo cannot perform 1st.
- Go back to his very first rule: "Leo will perform either 1st or 4th."
- Since we just proved he can't be 1st, there is only one possible truth left. Leo MUST perform 4th.
Let's look at what the timeline actually looks like:
[ 1st ] [ 2nd ] [ 3rd ] [ 4th ]
___ ___ ___ LEO
We don't know the exact order for Maya, Ned, or Olivia—and the test doesn't want us to know! Option B is the only fact we can prove with 100% certainty.
🧠 The "Repeatable Approach" for Ordering Puzzles
When you see a puzzle with times, days of the week, or 1st/2nd/3rd places:
- Ditch the Grid: Draw a simple blank timeline.
- Write the "NOTs" underneath: If someone cannot go on Tuesday, write "(Not X)" under Tuesday. This acts as a landmine.
- Run the Domino: Push the first "If" rule. Your goal is to see if the chain reaction accidentally pushes someone onto a landmine. If it does, you've found the crash!