Three Rooms

Logic Level 1

There are $3$ plain rooms, where each room only contains a group of people. $A$ resides in the $\text{1st}$ room, $B$ resides in the $\text{2nd}$ room, and $C$ resides in the $\text{3rd}$ room.

$A$ says: "I see $16$ eyes in this room."

$B$ says: "There are $9$ of us in this room."

$C$ says: "I count $10$ hands including my own in this room."

How many people are in the rooms in total?

Assume that all people in the rooms have a pair of hands and eyes, everyone is facing each other.

Another interesting problem

26 24 23 25 22

1 solution

Just C
Apr 26, 2021

Since $A$ cannot see his/her own eyes and sees $16$ eyes, there must be a total of $\displaystyle{16\over{2}} + 1 = 9$ people in the $\text{1st}$ room. $B$ directly tells us that there are $9$ people in the $\text{2nd}$ room. $C$ tells us there are $\displaystyle{10\over{2}}=5$ people in the $\text{3rd}$ room. Therefore, there is a total of $9+9+5=\boxed{23}$ people.

You may want to explain that we have to assume that every person in the first room has two eyes and every person in the third room has two hands (and perhaps that there are no animals in these rooms either?)

Chris Lewis - 1 month, 2 weeks ago

1) 'perhaps that there are no animals in these rooms either': I think this isn't an issue as I specified 'where each room has a group of people'

2) 'assume that every person in the first room has two eyes and every person in the third room has two hands': fair enough 😂 , didn't think of that issue, but I was hoping people would assume that in the first place.

I added it to the Q anyhow. Thanks!

Just C - 1 month, 2 weeks ago

"Each room has a group of people" does not mean there are no animals! (And, of course, how many people are facing the right way?? ;-) ).

Chris Lewis - 1 month, 2 weeks ago

@Chris Lewis – Fixed both! Don't think there are any flaws with the problem now. :)

Just C - 1 month, 2 weeks ago

I hope those people have 3 eyes each

Ash Ketchup - 1 month, 1 week ago

cool question!

Peporella ;) - 1 month, 1 week ago

WHAT IF SOME PEOPLE ARE HIDING???

Ash Ketchup - 1 month ago

Three Rooms

1 solution

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