Did You Know the ABC?

Logic Level 1

Three friends, Anna, Carla and Beth chose the letters A, B and C at random. The girl who chose C always lie, and the other two always tell the truth.

And Anna said:

"I chose B."

Then one of them who chose A said (can be anyone of them, even if she has already spoken):

"I'm not Beth."

And finally Beth said:

"Carla chose B."

Who chose C?

Beth Ana Carla

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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3 solutions

Denton Young
Sep 25, 2015

Anna chose either B or C (she couldn't have chosen A, because then she wouldn't have lied and said she chose B.)

The one who chose A, thus telling the truth, says she isn't Beth. Since Anna didn't choose A, Carla must have chosen A.

Therefore, Beth lied when she said Carla chose B. So Beth chose C.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Diana Paleracio
Sep 7, 2015

Anna Chose B; someone who chose A said she is not Beth;Beth said Carla chose B. Only one of them who tells lie. Anna chose B then the one who chose A either Anna or Carla. And Beth said Carla chose B. Then if is Anna saying the truth that she chose B then the one who chose A is Carla then Beth said Carla chose B is the one lie. Therefore, Beth is the one who chose the C.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Saya Suka
Feb 16, 2021

Anna admitted to have chosen B while Beth said that it was Carla who chose B. Then, Beth must have chosen either A or C. Either way, Beth would be lying (as one would expect from options between A's "I'm NOT Beth" or the fact that the girl who chose C always lie). Thus, Beth must have chosen C, Carla A and Anna B.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

A : I'm not Beth.
A can't lie, so A can't be Beth. Also, A can't be Anna who supposedly already lied by admitting to be B. A must be Carla, and Beth who lied about it must have chosen C.

Saya Suka - 3 months, 1 week ago

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