Let f
0(x)= x/(3x+2)
and, f
n(x)= f
0(f
n-1(x)), n≥1
Given that
f2018(x)= x/(Ax+B)
Determine the value of 3B-A
Note: Adapted from a problem appearing in Round 1 of Singapore Mathematical Olympiad Open 2018.
You're standing in front of a square mirror that's 300 mm on a side. There's a tiled wall behind you in which the tiles are squares 150 mm on a side. When you look in the mirror, you see exactly 25 of these tiles--or rather you would, if your body didn't get in the way of some of them.
Without being told the width of the room, identify what fraction of the way from the mirror to the tiled wall that you are located.
Latest: 