Problema Solution
There are 8 rooms (A-H) in a square. There are 4 one way mirrors in the center. The first mirror faces rooms A, B,C. The second mirror faces C, E, H. The third mirror faces H, G, F. The fourth mirror faces F, D, A. Place 22 students in the eight rooms so each mirror can see 9 students.
Answer provided by our tutors
We will assume that each set of three rooms has the same combination of numbers of people in the rooms such that one has x number of people, one has y number of people, and one has z number of people. We note that the order will probably be varied.
Rooms D, G, B, and E are each only seen through one mirror. Because of this, we will assume that they are all equal and we will denote them as x. Likewise, we can pair up A and H as y and C and F as z. From this we can write:
x+y+z=9
4x+2y+2z=22
However, this leaves us with three unknowns and only 2 equations. Therefore, we will assume y=z to get:
x+2y=9
4x+4y=22
Using Algebrator to solve, we get:
x=3.5
y=2
Since we need whole numbers, we reintroduce the 'z' variable and shift some number to get:
x=2
y=3
z=4
We plug it in to see if it works:
4(2)+2(3)+2(4)=22
2+3+4=9