On Planet Rho, there live two kinds of people, the Alpha and Omega. The Alphas tell only truths and the Omega tell only lies. However, they may, at midnight of every day, switch from one type to another, but that is only if they are inside what they call the “switch circle”, which I shall not explain in detail.
On the rival planet, Kappa, there live two kinds of people, the Beta and the Zeta. The Beta are sworn enemies of the Alpha and Omega, but and they can either lie or tell the truth.
The Zetas are a more complicated case which I will explain later. All I will tell you for now is that they always make more than one statement a time.
Round 1: Who is lying?
It is given that A, B and C are telling the truth.
A: B is either an Alpha or an Omega.
B: K believes that C is an Omega.
C: I am not an Omega, but K is.
D: J believes that K believes that E believes that G is an Omega.
E: C and L are either both Omega or both Alphas.
F: E is an Omega and G is an Alpha.
G: B believes that E believes that D believes that L believes that I believe that I am truthful.
H: Either A or G is correct, or maybe both.
M: I am an Alpha, B is an Omega and L is an Alpha.
J: I believe that I believe that I believe that I believe that I am an Omega.
K: At least eight of the above statements are correct.
L: I am not lying. E is an Alpha and H is an Omega.
Who is lying?
Round 2: Enter the Beta!
In two years, the twelve people have changed so much that it is impossible to tell if they are Alphas or Omegas. However, Rho has come under the threat of the planet Kappa, with Betas as inhabitants. Also, one of them has sided with the Betas and become one, and is working as a Beta for them!
One note: Betas can either lie or tell the truth, but only once at a time. And only six of the twelve are Alphas now.
In this Round, the people are questioned in groups of 6.
Group #1
A: F is the Beta.
C: A is the Beta.
G: D believes F is the Beta.
E: H believes both A and G are spies.
M: G is not a Beta.
K: I tell the truth.
Group #2
B: I am the Beta.
D: That is true.
H: I am not the Beta.
F: K believes H is a Beta. I am not a Beta.
J: Either K or F tells the truth, and maybe both.
L: Both B and D believe I am the Beta.
Your job is to figure out:
1. Who is the Beta?
2. Who remained the same?
Round 3: The Trial
X was put on trial with another person, Y. Unknown to the court, X was a Beta, but he did not show it.
They made the following statements:
X: Y is a Beta.
Y: X is a Omega.
X: Y is a Alpha.
Y: I am the Beta.
X: I am the Beta.
Y: You are a Alpha.
“First witness!” called the judge.
Z: X is a Beta.
Z: Both of them are spies.
Z: I am not a Beta.
Y: Z is a Beta and I am a Alpha.
X: Z is a Omega and I am a Beta.
Z: I am a Alpha and Y is a Omega.
Y: Z is a Alpha and I am a Beta.
X: Y is a Omega and Z is a Beta.
Who is/are the Beta/Betas?
Round 4: The metapuzzle
In the jail, Y was found badly beaten up. The three suspects were the guard, X and Z.
Guard: I beat him up.
X: I beat him up.
Z: I beat him up.
Suddenly, the midnight bell rang and the Guard gave a start. He had been standing in a “switch circle”.
Guard: That is not true!
X: That is not true!
Z: That is not true!
Knowing that each of them made one true and one false statement, who was the culprit?
Note that the Guard is not a Beta, he is a person working as a guard, and he changed sides during the bell.
Round 5: The Zeta’s Trial
The Zeta have not been prevented from travelling to and fro between the planets, as they do not pose a threat to the people. Most times, they are arrested for small crimes such as petty theft, etc.
They are governed by these rules:
1. He/she makes two or three statements at a time.
2. The first statement is of opposite polarity to the rest of the statements he/she makes.
3. All Zetas are human.
By these rules, it is possible for a Zeta to make two contradicting statements, for example:
1. I am a unicorn.
2. I am a human.
3. I am a Zeta.
In a court case on Planet Rho, three Zetas were being tried for stealing a mobile phone.
They made these statements:
A: I stole it!
I didn’t steal it!
B stole it!
B: I stole it!
I didn’t steal it!
C did not steal it!
C: A stole it!
B stole it!
I stole it!
Round 6: Who is the Zeta?
There is a Alpha, a Omega and a Zeta in trial and they made these statements:
A: I am guilty.
That statement was true.
B is guilty.
B: I am not guilty.
That statement was true.
C is guilty.
C: I am not a Zeta.
I am guilty.
That statement was true.
1. Who is the Zeta?
2. Who is guilty?
Round 7- Another problem!
In this problem, there is one of each of the races. One is guilty and another is a Beta.
Each of them made two statements, separately.
A: B is guilty.
B: C believes D is guilty.
C: D believes A is guilty.
D: A believes B is guilty.
A: I am not the Beta.
B: I am the Beta.
C: I am the Beta.
D: I am the Beta.
1. Who is the Beta?
2. Who is guilty? ¢
Round 8- The witnesses are…
In this trial, nobody knew of the identity of the witnesses except themselves, but the court wanted to find out what they were, so they made the witnesses give statements. One was a Alpha, one was a Omega and one was a Beta.
It is given that there were no more than one Beta in the courthouse, and he was one of the accused.
Trial Day 1
Suspect A: I am a Alpha.
Suspect B: I am not a Omega.
Suspect C: I am a Beta.
Witness A: Suspect C is a Omega.
Witness B: Suspect B is a Beta.
Witness C: Suspect A is a Omega.
Trial Day 2
Suspect A: I am not a Omega.
Suspect B: C is a Beta.
Suspect C: A is a Omega.
Witness A: Suspect B is a Omega and Witness B is a Beta.
Witness B: Suspect A is a Alpha and Witness A is a Alpha.
Witness C: Suspect C is a Beta and I am a Alpha.
What are the witnesses?
And who is the Beta?
Round 9- Two statements each
B: A is a Omega.
C: B is a Beta.
Judge: __, you are not the Beta, so you may leave.
Remaining #1: #2 is not the Beta.
Remaining #2: #1 is not the Beta.
Who is the Beta?
Round 10- And the criminal is…?
On Rho, a murder has just taken place, and reliable witnesses who are Alphas say that an Omega and an Alpha teamed up to kill the person. In all, six suspects were arrested, three Omega and three Alpha.
A: I did not kill him!
B: I did not kill him!
C: A and E did it!
D: A and B did it!
E: A did it!
F: B and E did it!
Who did it?
Round 11: More suspects
This time, there are eight suspects, half Alpha and half Omega. Each makes two statements.
A: B is a Omega.
B: C is a Alpha.
C: D is a Omega.
D: E is a Alpha.
E: F is a Omega.
F: G is a Omega.
G: H is a Omega.
H: A is a Omega.
A: B did it!
B: C did it!
C: D did it!
D: E did it!
E: F did it!
F: G did it!
G: H did not do it!
H: A did it!
Who did it?
Round 12- The last problem
This time, there are four culprits out of ten! They will make two statements each.
B: E is a Omega.
C: F is a Alpha.
D: G is a Alpha.
E: H is a Alpha.
F: M is a Omega.
G: J is a Omega.
H: A is a Omega.
M: B is a Alpha.
J: C is a Alpha.
A: H did it!
B: M did not do it!
C: J did it!
D: A did it!
E: B did it!
F: C did not do it!
G: D did it!
H: E did not do it!
M: F did not do it!
J: G did not do it!
A: I did not do it!
Who did it?
Round 13- The end of the day!
“Good evening dear,” said the judge’s wife.
“Good evening.” said the judge. “Could you cook some dinner for the two of us, please?”
“Of course! Actually, I’ve already cooked it, but you’ll have to solve this problem first.”
“Oh, not again!”
There are three people- a Alpha, a Omega and a person of unknown race. They make one or more statements each:
A: The dinner is in the first box.
B: The dinner is not in the second box.
C: The dinner is not in the third box.
A: The dinner is in the third box.
Can you solve this problem?
Shao Wei
3:27 PM