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

Spread the love

[ad_1]

I’ve heard and thought about variants of this puzzle several times, and they always remind me of the tragedy of Amelia Earhart. She and her navigator Fred Noonan disappeared in 1937, while trying to fly around the world in a Lockheed Electra. Did she run out of fuel? Did something go badly wrong with the Electra? There has been no trace of either the plane or its occupants in these 84 years.

They were last seen at Lae Airfield in Papua New Guinea. So in a tribute to Earhart and Noonan, this puzzle is set there.

Assume Lae has a large number of identical Lockheed Electras that fly at identical speeds. It also has a huge store of aircraft fuel. With a full tank of fuel, each Electra can fly exactly halfway around the world (assume a “great circle” route, meaning the shortest possible circumnavigation). What’s more, these Electras are different from Earhart’s model in that they can be refueled in flight by another Electra. Doing so, we’ll assume, is instantaneous, doesn’t slow either plane down, or use any extra fuel. If a plane has no fuel, it can keep flying if it is being refueled. But you should note that the only place you can get fuel is Lae itself, and refueling there is also instantaneous.

Question: You want one Electra to do the full circumnavigation of Planet Earth, without landing anywhere else, and return to Lae. What’s the minimum number of Electras you need to accomplish this? How will they do it? Needless to say, all Electras that take off must return safely to Lae.

Hint: Try three Electras, for example. Call them Amelia, Fred and (why not) Ramanujan. Fill all three with fuel and send them off with plenty of fanfare. Do you need more Electras?

Scroll down for the answer.

.

.

.

.

.

.

.

.

.

.

Answer:

Break the journey into eighths:

1/8 complete: All three have used up 1/4 of their fuel. Fred refuels Amelia and Ramanujan with 1/4 tank each. Both are now full. Fred has 1/4 tank, enough to return to Lae.

1/4: Amelia and Ramanujan, both 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 other way around the great circle.

5/8: Amelia 1/4 tank. Fred and Ramanujan are at the 7/8 point, 3/4 tank each. 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 again.

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 done the circumnavigation. Three planes are enough!

[ad_2]

Source link

Tags:

88 thoughts on “A fanciful flight plan: The Wknd Puzzle by Dilip D’Souza

  1. Handoko ML, Lamberts RR, Redout EM, de Man FS, Boer C, Simonides WS, Paulus WJ, Westerhof N, Allaart CP, Vonk Noordegraaf A There have been many steroids that have come and gone since Nandrolone first hit the shelf yet Nandrolone always remains

  2. As a result, frequent doses at 3 to 4 hour intervals are necessary to maintain the therapeutic effect cialis vs viagra Taxane therapy, for example, requires premedication but premedication does not prevent true type I reactions to the platin drugs 24

  3. As far as the GHO stablecoin is concerned, Aave Companies said that the community was “very engaged with the GHO proposal, providing incredibly helpful and informative feedback.” Aave detailed some of the things mentioned by the community the team will focus on which includes DAO-set interest rate vulnerabilities, supply caps, a peg stability module, and the “necessity for properly vetting potential facilitators.” For now, the community will have to participate in voting on the stablecoin’s genesis parameters before the crypto token is issued. AAVE is a native coin of the Aave project that was launched in 2017 under the name ETHLend and was later rebranded. Aave is a decentralized lending protocol built on Ethereum and uses decentralized autonomous organization (DAO). Meaning, it is governed and operated by AAVE token holders who vote on changes to the protocol.
    http://xn--vk1b511aoves4i.kr/bbs/board.php?bo_table=free&wr_id=30012
    Whenever you’re selecting a broker, it’s important to consider all of your needs. And for new traders in cryptocurrency, you’ll want to figure out whether you want to own the virtual currency directly or whether you want to trade futures, which offer higher reward, but also higher risk. TD Ameritrade, Inc. and all third-parties mentioned are separate unaffiliated companies and are not responsible for each other’s services or policies. Crypto exchange-traded funds (ETFs) and index funds are investment vehicles that provide exposure to a basket of cryptocurrencies or a single cryptocurrency. They are designed to track the performance of a specific index, benchmark or cryptocurrency, and they allow investors to gain exposure to the crypto market without having to purchase and manage multiple coins.

  4. Thank you for the auspicious writeup. It if truth
    be told used to be a enjoyment account it. Glance complicated to far introduced agreeable from you!

    By the way, how could we be in contact?

  5. I am really impressed with your writing abilities and also with the format
    in your weblog. Is this a paid subject or did you customize it your self?

    Anyway keep up the excellent quality writing, it’s rare to look a great blog like this one nowadays..

  6. Its like you read my mind! You seem to know a lot about this, like you
    wrote the book in it or something. I think that you can do
    with a few pics to drive the message home a bit, but other than that, this
    is wonderful blog. An excellent read. I’ll certainly be back.

  7. For most up-to-date information you have to pay a visit the web and on the web I found this web page
    as a most excellent web site for latest updates.

  8. Thank you for sharing your info. I truly appreciate your
    efforts and I will be waiting for your next post thank you
    once again.

  9. I’m not that much of a online reader to be honest but
    your blogs really nice, keep it up! I’ll go ahead and bookmark your website to come back later on. Cheers

  10. Excellent goods from you, man. I’ve understand your stuff previous
    to and you are just too excellent. I actually like what you have acquired here,
    certainly like what you’re saying and the way in which you say it.
    You make it entertaining and you still take care of to keep
    it sensible. I cant wait to read far more from you.
    This is actually a great site.

  11. Hi, I think your site might be having browser compatibility issues.
    When I look at your website in Chrome, it looks fine but when opening in Internet Explorer, it
    has some overlapping. I just wanted to give you a quick
    heads up! Other then that, excellent blog!

  12. Spot on with this write-up, I absolutely believe this amazing
    site needs a lot more attention. I’ll probably be returning to see more,
    thanks for the information!

  13. This is very interesting, You’re a very skilled blogger.
    I have joined your feed and look forward to seeking more of your excellent post.
    Also, I have shared your site in my social networks!

Leave a Reply

Your email address will not be published. Required fields are marked *