Survival

A forum for good logic/math puzzles.

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Jayraj
Posts: 15
Joined: Sun Oct 21, 2018 11:06 am UTC

Survival

Once upon a time you along with some passengers huddle together and weather the storm until the next morning.

When you awaken, you find the skies have cleared and you have come ashore on what seems to be a recently deserted island.

You explore a bit and come across an abandoned military camp, which you search through for supplies.

Notably, you find the keys to a nearby truck, 300 liters of gasoline in a cemented tank, some empty gas canisters strewn about and a diary.

You go through the diary, and find that it is a manifest of all items that were shipped from the island and what remains here.

It shows that there is a radio outpost on a nearby plateau, with functioning equipment and a shipment of juice.

You can see the antennas on the top of a nearby plateau, but you are all tired and cannot walk uphill.

You inspect the truck and find a note scribbled on its dashboard saying:

1. EXTREME OFFROAD ROUTE - DO NOT TRANSPORT GASOLINE ONBOARD!!!

2. Fill up the 30L inbuilt tank.

3. Attach a FULL 70L gas canister in the provided slot.

4. The full journey of 288km will consume the full 100L of gas.

Sure enough, the canisters you found earlier fit in the correct slot and are of the required capacity.

You do not know what awaits you atop the plateau, and you want to transport as much gasoline as possible to the radio outpost.

Devise a plan. What is the maximum number of liters of gasoline you can save for later?

Note:

While travelling downhill, your truck does not consume any gas.

Gas consumption does not vary with load nor road conditions (downhill :- 0 consumption, uphill :- constant consumption).

There are no other ways to transport gasoline aside from the gas canisters within the provided slot.

The truck is large enough to accommodate all of you.

Tirear
Posts: 35
Joined: Fri Feb 05, 2016 5:42 pm UTC

Re: Survival

Spoiler:
Use 100L to fill the engine and attached canister. Drive 50L worth uphill, remover canister with remaining 50L. Return. Use another 100L to fill engine and another canister which you attach. Drive 75L worth uphill, remove canister with remaining 25L. Return. Use final 100L to fill engine and another canister which you attach. Drive 50L worth uphill, use the canister there to fill engine and attached canister to full. Drive another 25L worth uphill, use the canister there to fill engine and attached canister to full. Drive final 25L worth uphill, reaching plateau with 75L remaining.

Leaving gas further in the route means wasting gas carrying the remainder further than you need it. Leaving it earlier in the route means you won't have room to use it all when you next reach that spot, but we could probably do partial refills in more than one trip. Okay, returning with gas in the tank would be wasteful, so we still have three trips. First trip goes 1/3rd up, leaves the remaining 2/3 there. Second trip refills there, goes another 50L worth, leaves 50L worth. Final trip is therefore full 5/6ths of the way up, so it reaches the top with 5/6th of the fuel, or just over 83L.

Carrying the fuel any further means wasting fuel. Carrying it less far means not being able to use all the fuel on future trips without wastefully backtracking. I don't think it can get any better than this.