Answer
$5~~$ is the minimum number of sheets required if the transmitted intensity is to be more than 60% of the original intensity.
Work Step by Step
Suppose there are $n$ sheets and each sheet is angled at $\frac{90^{\circ}}{n}$ to the previous direction of polarization.
We can write an expression for the intensity of the light that is transmitted:
$I = I_0~cos^{2n}~\frac{90^{\circ}}{n}$
When $n = 1$:
$I = I_0~cos^2~\frac{90^{\circ}}{1} = 0$
When $n = 2$:
$I = I_0~cos^4~\frac{90^{\circ}}{2} = 0.25~I_0$
When $n = 3$:
$I = I_0~cos^6~\frac{90^{\circ}}{3} = 0.42~I_0$
When $n = 4$:
$I = I_0~cos^8~\frac{90^{\circ}}{4} = 0.53~I_0$
When $n = 5$:
$I = I_0~cos^{10}~\frac{90^{\circ}}{5} = 0.61~I_0$
$5~~$ is the minimum number of sheets required if the transmitted intensity is to be more than 60% of the original intensity.
