A whimsical flight plan: The Wknd Puzzle by Dilip D’Souza

I’ve heard and thought of variants of this puzzle a number of instances, and so they at all times remind me of the tragedy of Amelia Earhart. She and her navigator Fred Noonan disappeared in 1937, whereas making an attempt to fly world wide in a Lockheed Electra. Did she run out of gas? Did one thing go badly unsuitable with the Electra? There was no hint of both the aircraft or its occupants in these 84 years.

They had been final seen at Lae Airfield in Papua New Guinea. So in a tribute to Earhart and Noonan, this puzzle is about there.

Assume Lae has numerous similar Lockheed Electras that fly at similar speeds. It additionally has an enormous retailer of plane gas. With a full tank of gas, every Electra can fly precisely midway world wide (assume a “nice circle” route, which means the shortest doable circumnavigation). What’s extra, these Electras are totally different from Earhart’s mannequin in that they are often refueled in flight by one other Electra. Doing so, we’ll assume, is instantaneous, doesn’t gradual both aircraft down, or use any additional gas. If a aircraft has no gas, it might probably hold flying whether it is being refueled. However you need to notice that the one place you may get gas is Lae itself, and refueling there may be additionally instantaneous.

Query: You need one Electra to do the total circumnavigation of Planet Earth, with out touchdown anyplace else, and return to Lae. What’s the minimal variety of Electras you want to accomplish this? How will they do it? Evidently, all Electras that take off should return safely to Lae.

Trace: Attempt three Electras, for instance. Name them Amelia, Fred and (why not) Ramanujan. Fill all three with gas and ship them off with loads of fanfare. Do you want extra Electras?

Scroll down for the reply.

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Reply:

Break the journey into eighths:

1/8 full: All three have used up 1/4 of their gas. Fred refuels Amelia and Ramanujan with 1/4 tank every. Each at the moment are full. Fred has 1/4 tank, sufficient to return to Lae.

1/4: Amelia and Ramanujan, each 3/4 tank. Ramanujan to Amelia, 1/4 tank. Amelia full. Ramanujan 1/2, returns to Lae. Fred lands at Lae, refuels and waits.

3/8: No change.

1/2: Amelia 1/2 tank. Ramanujan at Lae, refuels. Fred and Ramanujan take off, flying the opposite manner across the nice circle.

5/8: Amelia 1/4 tank. Fred and Ramanujan are on the 7/8 level, 3/4 tank every. Fred to Ramanujan, 1/4 tank. Ramanujan full. Fred 1/2 tank, returns to Lae.

3/4: Amelia 0, meets Ramanujan, 3/4 tank. Ramanujan to Amelia, 1/4 tank. Ramanujan 1/2 tank, turns for Lae. Fred at Lae, refuels and takes off once more.

7/8: Amelia 0, meets Fred, 3/4 tank. Fred to Amelia, 1/4 tank. All three head for Lae.

Lae: All three land safely. Amelia has executed the circumnavigation. Three planes are sufficient!

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