I13-01

Question

Alex, Billy, Charlie and Derrick are the leading environmentalists in Pinaka, a country with only 20% of the land under forest. All four are often seen together in various seminars delivering lectures on environmental issues. In one such seminar on environmental sustainability, the first four slots for speakers were reserved for them. Due to prior commitments, Derrick showed his inability to speak in any of the first three slots and picked up the fourth slot.
 
When the organizers inquired about the sequence for remaining three, the following three statements were made by the environmentalists with the caveat that only one of them is speaking the truth.
 
Alex: “Billy is the first speaker”.
 
Billy: “Charlie is not the first speaker”.
 
Charlie: “Alex is not the third speaker”.
 
Select for  First Speaker  the environmentalist who has to deliver the first lecture, and for  Third Speaker  the environmentalist who has to deliver the third lecture. Make only two selections, one in each column.

Bunuel · Answer

Official Solution:

We are given three statements, and only one of them is true.
 
1. Alex: “Billy is the first speaker.”
 
2. Billy: “Charlie is not the first speaker.”
 
3. Charlie: “Alex is not the third speaker.”
 
We also know that  Derrick is the fourth speaker .
 
 Step 1: Assume Alex's statement is true 
 
If Alex is telling the truth, then  Billy must be the first speaker .
 
Since only one statement can be true, Billy’s and Charlie’s statements must both be false.
 
If Billy’s statement  “Charlie is not the first speaker”  is false, then Charlie  must be the first speaker . However, this directly contradicts our assumption that Billy is the first speaker.
 
This contradiction proves that Alex’s statement  must be false .
 
 Step 2: Assume Billy's statement is true 
 
If Billy is telling the truth, then  Charlie is not the first speaker .
 
Since only one statement can be true, Alex’s and Charlie’s statements must both be false.
 
Alex’s statement  “Billy is the first speaker”  is false, meaning Billy  is not  the first speaker.
 
If neither Charlie nor Billy is the first speaker, then Alex must be the first speaker. However, if Alex is the first speaker, then Charlie’s statement  “Alex is not the third speaker”  would also be true, contradicting the rule that only one statement can be correct.
 
This contradiction proves that Billy's statement  must be false .
 
 Step 3: Analyze Charlie’s statement 
 
If Charlie is telling the truth, then  Alex cannot be the third speaker .
 
Since only one statement can be true, Alex’s and Billy’s statements must both be false.
 
Alex’s statement  “Billy is the first speaker”  is false, meaning Billy  is not  the first speaker.
 
Billy's statement  “Charlie is not the first speaker”  is false, meaning Charlie  must be the first speaker .
 
With Charlie as the first speaker and Alex not in the third slot, he must take the second slot, leaving Billy as the third speaker. This results in the order:  Charlie - Alex - Billy .

Correct answer:

First Speaker  "Charlie"

Third Speaker  "Billy"

Bunuel · Answer

I have revised the question, solution, and formatting by adding more details to enhance clarity.

Aditya00799 · Answer

intresting question

ravitejab1 · Answer

I like the solution - it’s helpful.

Dream009 · Answer

the trick here is that both Alex and billy are talking about the first speaker and both of them can/t be opposing.
Eg if Alex is true -> and Billy is first speaker 
Billy will be a liar -> But his statement will turn out to be true - that charlie is not first. So they both should be 1 side and since there is only 1 truth teller both are liars.

KarthikRajP · Answer

This is a great question that’s helpful for learning.

agrasan · Answer

I like the solution - it’s helpful.

RishabhAggarwal · Answer

Does false here mean the exact opposite/logical negation of the statement? This is a bit distorting. Generally, false is not equivalent to negation of the statement.

Bunuel · Answer

Here, false means the opposite of what was said.

I13-01

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First Speaker	Third Speaker
		Alex
		Billy
		Charlie
		Derrick
		Cannot be determined