You had been certainly one of $n$ contestants chosen to take part in a recreation present. Each of you’ll secretly choose a resistor of your alternative, with a resistance between 0.01 and 10,000,000 ohms. Once everybody has made their alternative, the resistors shall be revealed, related in sequence, and connected to an excellent 240 volt energy provide. Each contestant will then be paid $1 per watt of energy that their resistor dissipated, rounded to the closest cent.

For instance, assume that $n = 3$, you selected a 2.2 ohm resistor, and the opposite contestants selected a 4.7 and 6.8 ohm resistor. You’d win $675.16, and so they’d win $1,442.38 and $2,086.85, respectively.

Contestants might discuss to one another at any time throughout the recreation, however usually are not required to be truthful. If you need to win as a lot cash as attainable for your self, and are detached to what anybody else wins, what do you have to do? Note that the reply is determined by the worth of $n$.

Hint:

The rounding of the prize cash is necessary. The greatest technique can be qualitatively completely different if it weren’t rounded.