Crossposted from
advancednanoSome people have said that the Google Lunar Xprize cannot be won I think winning the prize is doable. Note: the people (Spaceshipone) and teams who tried to win the last xprize collectively spent more than the prize amount. The winners alone spent 2.5 times the prize the amount.
$10 million to get to orbit with a Dnepr rocket. (A cheap SpaceX falcon launch is also possible) The rules do not say that you have to make your own rocket.
550 kg (with ST-1) to Trans Lunar Injection. Not sure how much the ST-1 stage costs. Probably better to just take the basic rocket to ISS level or slightly higher orbit with about 3000kg and then try to use low energy maneuvers from there.
Probably would have to use the
Interplanetary transport network for lower power movement between the earth and the moonA low energy transfer was achieved from the earth to the moon using the Japanese satellite Hiten 
The Hiten spacecraft that made it from earth orbit to lunar orbit
Description of the three body method to get to the moon with one tenth the fuel or using ion drive propulsion 
The basic look of the low energy solution route
There has been a fair bit of theoretical work on the
interplanetary low energy gravitional tube system Hiten weighed about 197kg fully fueled A slow 5 month maneuver. You are then in lunar orbit. 500-2000kg.

the old lunar LEM, descent module was 10 tons but it was carrying the 5 ton ascent module.
You make a small descent lander. You can make it smaller than Apollo LM modules. No need to carry ascent module down. No need to carry two astronauts or life support.
Mars Sojourner weighed about 11kg.
You need to make a lineup the Dnepr ride, orbiter stage, plan out the low energy transfer from earth to lunar orbit, descent module and a rover.
There is already a Nasa challenge on the lunar lander. Armidillo seems likely to win that.

the Armidillo lander, which was developed for the 2 million lunar lander challenge
From the xPrize site: The hover times (for the lunar lander challenge) are calculated so that the Level 2 mission closely simulates the power needed to perform the real lunar mission.
So putting this together rocket to orbit, earth orbit to lunar orbit low energy transfer, lunar lander and rover is just a matter of assembling the pieces. My bet is that Armidillo Aerospace can win the Google challenge. The question is why NASA is not sending a constant stream of larger robot vehicles to the moon now using low energy transfers. There should also be ion drive tugs going between the earth and the moon and back again.
FURTHER READING
Google's blog discusses the reasons for Google's sponsorship of the prize