First, majority of contestants are probably more used to solving electrodynamics problems rather than problems on heat conductivity, I recommend mapping the thermodynamics problem onto electrostatics problem (use your mapping to express the final answer for the thermodynamics problem on the basis of the answer for the corresponding electrostatics problem).
Second, my own solution was using electrical images, but more than half of the correct solutions did not use it (some of these were very nice!). There are many different approaches which are all correct and lead to the correct answer.
