Wizard's Quiz

Since the coins are identical, so their weight depends on their densities. Arranging the metals in increasing order of their densities: $Zn<Fe<Cu<Ag<Au<Pt$ According to wizard Zinc should have the least value while Platinum the most.

The values are in AP .

Let the AP be: $a-5d,a-3d,a-d,a+d,a+3d,a+5d$ & $\ce{S6}=240=a-5d+a-3d+...+a+5d$ $\Rightarrow 240 =6a$ $\Rightarrow \boxed{a=40}$ It is given that: $\frac{\ce{a1}\times\ce{a6}}{\ce{a2} \times\ce{a5}} = \frac{375}{1159}$ $\Rightarrow \frac{(40-5d)(40+5d)}{(40-3d)(40+3d)}=\frac{375}{1159}$ $\Rightarrow \frac{1600-25d^2}{1600-9d^2}=\frac{375}{1159}$ $\Rightarrow d=\pm7$ In order to make Zinc with least value $d$ is to be positive.

So $\boxed{d=7}$

& The AP is $5,19,33,47,61,75$ Gold coin's value is at $\ce{a5}$

So the value of Gold coin is $\boxed{61}$ .