CAOS Astro-Math
Brain Warm-up Provided by Peter Lamonica
The Russians are shuttling astronauts to the International Space Station (ISS) while the USA’s Space Shuttle Program is under review. Unfortunately, the Russian Space Agency (RKA) has fallen upon hard times itself and so must place the following restrictions on its mission. Your task is to plan a series of steps that will get all four astronauts to the ISS.
  1. The RKA has only one shuttle but can use it many times for this mission.
  2. The RKA’s shuttle can carry only two astronauts at a time (a driver and a passenger.)
  3. The shuttle has no auto-pilot and so must have a driver for each part of the mission.
  4. The RKA has only 14 units of fuel allocated for this mission.
  5. Contrary to any physical explanation, the shuttle must consume one unit of fuel for each unit of weight of the HEAVIEST of the two astronauts. Thus if a 5 unit astronaut and a 4 unit astronaut travel then the trip will take 5 units of fuel.
  6. Inexplicably, rule 5 also applies to return trips. However, you will most likely send only one astronaut back with the shuttle each trip so his/her weight will determine the fuel consumed.
  7. The four astronauts weigh 1, 2, 5, and 7 units and their names are 1, 2, 5, and 7 respectively ;)
  1. sunil (solved: 1-10-2005 10:14am)
  2. tom von kercey (solved:1-10-2005 5:53pm)
  1. 14 Units Remain
  2. 1 & 2 Travel Up 12 Units Remain
  3. 2 Travels Back 10 Units Remain
  4. 5 & 7 Travel Up 3 Units Remain
  5. 1 Travels Back 2 Units Remain
  6. 1 & 2 Travel Up 0 Units Remain
The trick to this problem is recognizing that since only the heaviest astronaut counts you should find a way to send the heaviest and second heaviest astronauts in the same trip. If you try and do this in the first trip then one of them two will have to bring the shuttle back to the surface and will defeat any gain you got from sending them both at once. You cannot send them both in the last trip because one of the people involved in the last trip must have been on the station already to bring the shuttle back and this is just as bad as sending them both up at the start. Thus, you must send the two heaviest after one light astronaut is already on the station to make a return trip.
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