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Complete a loop of five large cities.

The starting city name starts with the letters MA. Each of the following cities starts with the last two letters of the previous city name. (Like PARIS ISTANBUL etc.). The fifth city name ends in MA, completing the loop.

All cities have population of at least 1 million according to many websites.

I understand there could be more than one answer. My answer has majority of cities from Asia.

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    $\begingroup$ I wonder what the longest such loop we can find? $\endgroup$
    – Dmitry Kamenetsky
    Commented May 31, 2021 at 14:17
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    $\begingroup$ @DmitryKamenetsky I was able to get 7 but one of them was not over 1 million. $\endgroup$
    – DrD
    Commented May 31, 2021 at 14:21
  • $\begingroup$ Do you have a list of available cities? I could write a program to search for the longest cycle. $\endgroup$
    – Dmitry Kamenetsky
    Commented Jun 1, 2021 at 9:46
  • $\begingroup$ @DmitryKamenetsky I looked at the attached list. data.mongabay.com/cities_pop_01.htm $\endgroup$
    – DrD
    Commented Jun 1, 2021 at 10:19
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    $\begingroup$ Manama (Bahrain) regrets that it has but 200,000 people, for it could save you a lot of travel. $\endgroup$
    – Jeremy Dover
    Commented Jun 1, 2021 at 20:41

4 Answers 4

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I came up with this, though I have to admit I had to check the number of inhabitants of the last one:

MAnilLA - LAgOS - OSaKA - KAracHI - HIroshiMA

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I used a depth-first-search program to find all possible chains of length 5. I used this list of cities: https://worldpopulationreview.com/world-cities

marseille leshan ankara ranchi hiroshima
matola lagos osaka karachi hiroshima
manila lagos osaka karachi hiroshima
ma'anshan antalya yaounde delhi hiroshima
ma'anshan anshan ankara ranchi hiroshima
malappuram amman ankara ranchi hiroshima
mashhad addisababa basra ranchi hiroshima
mashhad addisababa bamako kochi hiroshima

It is interesting that they all end with hiroshima.

For a bit of fun I also wanted to find the longest chain possible. I only ran it for a few minutes and I am sure longer chains are possible. I found one with 57 cities:

manila lahore recife fes esfahan antalya yaounde delhi hiroshima mashhad addammam amman anshan antananarivo volgograd adana natal aleppo porto tolucadelerdo douala lagos oslo lome merida dallas astana nairobi bishkek ekurhuleni ningbo bobo bogota tampico cordoba baoji jiddah ahmedabad addisababa baku kumasi siliguri riodejaneiro rome mecca casablanca cali lille leondelosaldamas asuncion onitsha hargeysa samarinda daegu guwahati tiruchirappalli lima

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  • $\begingroup$ The page you link to doesn't list Mexico, which you use. $\endgroup$
    – msh210
    Commented Jun 4, 2021 at 4:49
  • $\begingroup$ Also, this doesn't answer the question, which sought a loop of five cities. $\endgroup$
    – msh210
    Commented Jun 4, 2021 at 4:51
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    $\begingroup$ msh210 is right on that Mexico is not a city, but "Mexico City" is. $\endgroup$
    – justhalf
    Commented Jun 4, 2021 at 6:00
  • $\begingroup$ Thanks for the comments. I have fixed all the problems. $\endgroup$
    – Dmitry Kamenetsky
    Commented Jun 4, 2021 at 6:34
  • $\begingroup$ @NilayGhosh thank you! I like your answer too. $\endgroup$
    – Dmitry Kamenetsky
    Commented Jun 4, 2021 at 13:48
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Alas, I couldn't find a 5-city chain but I did find a 6-city chain.

Maracaibo -> Bogota -> Tangshan/Taiyuan -> Ankara -> Ranchi -> Hiroshima

Update: I found a 5-city chain but I tweaked a little bit. I used the old name for one of the cities:

Madras(old name for Chennai)-> Aswan -> Ankara -> Ranchi -> Hiroshima

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  • $\begingroup$ Hello @Nilay Ghosh. Rot 13 (Fgneg jvgu Znvqhthev, n Avtrevna Pvgl, naq lbh fubhyq trg vg va 5 fgrcf,) $\endgroup$
    – DrD
    Commented Jun 1, 2021 at 13:57
  • $\begingroup$ I had never heard of Ranchi, but using that, combining with my previous answer I could get to 7: ZNavyYN - YNtBF - BFnXN - XNmNA - NAxnEN - ENapUV - UVebfuvZN $\endgroup$
    – Bart-Jan van Rossum
    Commented Jun 1, 2021 at 14:47
  • $\begingroup$ @Bart-JanvanRossum Yes, you could go to seven. I have thought of another chain but one of them has below 1 million population. $\endgroup$
    – Nilay Ghosh
    Commented Jun 2, 2021 at 3:01
  • $\begingroup$ @DrD rot 13(Ohg znvqhthev unf cbchyngvba bs fvk uhaqerq gubhfnaq. ) $\endgroup$
    – Nilay Ghosh
    Commented Jun 2, 2021 at 5:44
  • $\begingroup$ Jung vf gur cbchyngvba bs Znvqhthev? Nafjre: Znvqhthev, Avtrevn (Nqzvavfgengvir havg: Obeab) - ynfg xabja cbchyngvba vf ≈ 1 112 400 (lrne 2015). Guvf jnf 0.611% bs gbgny Avtrevn cbchyngvba. Vs cbchyngvba tebjgu engr jbhyq or fnzr nf va crevbq 2006-2015 (+1.51%/lrne), Znvqhthev cbchyngvba va 2021 jbhyq or: 1 217 434*. This is from population.city web site. $\endgroup$
    – DrD
    Commented Jun 2, 2021 at 10:36
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Well, this answer is a bit of cheating since it uses a non-English spelling for one of the cities (however, the question does not explicitly state that the names of the cities should be in English):

Makka (native Arabic version of Mecca, Saudi Arabia - also spelled Makkah, but this is obviously unsuitable) -> Kazan (Russia) -> Ankara (Turkey) -> Ranchi (India) -> Hiroshima (Japan).

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    $\begingroup$ It's not just that that's not its English name. That's not its Arabic name either. That's a transliteration of its Arabic name. Its actual Arabic name is مكة‎. $\endgroup$
    – msh210
    Commented Jun 4, 2021 at 4:47

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