# Nothing but simple logic

#### mathmaniac

##### Well-known member
Three scholars are riding in a railway car. The train passes through a
tunnel for several minutes, and they are plunged into darkness. When they emerge,
each of them sees that the faces of his coll~agues are black with the soot that flew in
through the open window. They start laughing at each other, but, all of a sudden,
the smartest of them realizes that his face must be soiled too. How does he arrive
at this conclusion?

#### mathmaniac

##### Well-known member
Nobody can do this?

#### jakncoke

##### Active member
he touches his face?

#### Klaas van Aarsen

##### MHB Seeker
Staff member
Since they all start laughing they quickly realize that each of them sees at least one sooted face.

If there were two sooted faces, two of them would see only 1 sooted face.
These two would stop laughing then, knowing their face had to be sooted.

When after a while no one stops laughing, they realize all 3 faces are sooted and they stop laughing almost simultaneously.

When they have all stopped laughing they have confirmation for their analysis. $\quad \blacksquare$

#### mathmaniac

##### Well-known member
I like serena.....

But only one finds it because only he is a scholar....