I4.1 Suppose the 9-digit number $\overline{32 x 35717 y}$ is a multiple of 72 , and $P=x y$, find the value of $P$.
I4.2 Given that the lines $4 x+y=\frac{P}{3}, m x+y=0$ and $2 x-3 m y=4$ cannot form a triangle. Suppose that $m>0$ and $Q$ is the minimum possible value of $m$, find $Q$.

I4.3 Given that $R, x, y, z$ are integers and $R>x>y>z$. If $R, x, y, z$ satisfy the equation $2^{R}+2^{x}+2^{y}+2^{z}=\frac{495 Q}{16}$, find the value of $R$.

I4.4 In Figure $1, Q$ is the interior point of $\triangle A B C$. Three straight lines passing through $Q$ are parallel to the sides of the triangle such that $F E / / A B, G K / / A C$ and $H J / / B C$. Given that the areas of $\triangle K Q E, \triangle J F Q$ and $\triangle Q G H$ are $R, 9$ and 49 respectively. If the area of $\triangle A B C$ is $S$, find the value of $S$.
$72=8 \times 9$, the number is divisible by 8 and 9 . (Reference: 2001 FG1.3, 2017 HI1) $\overline{17 y}$ is divisible by 8 , i.e. $y=6$.
$3+2+x+3+5+7+1+7+6=9 m$, where $m$ is an integer.
$34+x=9 m, x=2$
$$
P=x y=2 \times 6=12
$$

Slope of $L_{1}=-4$, slope of $L_{2}=-m$, slope of $L_{3}=\frac{2}{3 m}$
If $L_{1} / / L_{2}: m=4$; if $L_{2} / / L_{3}: m^{2}=-\frac{2}{3}$ (no solution); if $L_{1} / / L_{3}: m=-\frac{1}{6}$ (rejected, $\because m>0$ )

Sub. into (3): $\frac{2 \times 4}{4-m}-\frac{3 m(-4 m)}{4-m}=4$
$3 m^{2}+m-2=0$
$(m+1)(3 m-2)=0$
$m=\frac{2}{3} \quad($ rejected $-1, \because m>0$ )
Minimum positive $m=\frac{2}{3}$
$$
2^{R}+2^{x}+2^{y}+2^{z}=\frac{495 \cdot \frac{2}{3}}{16}=\frac{165}{8}=20+\frac{5}{8}=2^{4}+2^{2}+\frac{1}{2}+\frac{1}{2^{3}}
$$
$R=4$
It is easy to show that all triangles are similar.
By the ratio of areas of similar triangles,
$$
\begin{array}{l}
S_{\triangle K Q E}: S_{\triangle J F Q}: S_{\triangle Q G H}=(Q E)^{2}:(F Q)^{2}:(G H)^{2} \\
4: 9: 49=(Q E)^{2}:(F Q)^{2}:(G H)^{2} \\
Q E: F Q: G H=2: 3: 7 \\
\text { Let } Q E=2 t, F Q=3 t, G H=7 t \\
A F Q G \text { and } B E Q H \text { are parallelograms. } \\
A G=3 t, B H=2 t \text { (opp. sides of } / / \text {-gram) } \\
A B=3 t+7 t+2 t=12 t \\
S_{\triangle A B C}=4 \times\left(\frac{12}{2}\right)^{2}=144=S
\end{array}
$$