Tag Archives: brainteaser

2017: Leonardo, Fibonacci and Fermat Numbers: It’s Not So Complicated.

In my previous post we had a math competition. Let me remind you of the task:

Using +, -, x, ÷ and (), make the row of numbers from 10 to 1 equal 2017.

That was an easy task, which got more complicated.

How about 9 to 1 with arithmetic equalling 2017? 8 to 1? 7 to 1? And down to just 1?

Before I could say ‘What January blues when you’ve got arithmetic in your life!?!’ I had answers from people in our fan club streaming in! And some of them (remember, there are different possibilities to get the same answer of 2017) were so wonderfully interesting, while others were so interestingly not-quite-elegant enough, that, well, I just had to share some of them with you…

Read on: A real math indulgent…

2017: Prime Numbers, Factorials, Primorials, Derangements: It’s Complicated.

As many will already know, the number 2017 is a prime number; that is, it can be divided without a remainder only by itself and 1. Must say, the theory of prime numbers is a wholly interesting one and an extremely useful one too, as any cryptographer will tell you :).

But today I’ll be writing about something different. See, based on the fact that 2017 is prime – or ‘simple’ – many, myself included, are anticipating a simple, straightforward and calm year 2017, especially since 2016 was a bit of a rotter. Let me show you why.

Like I said, prime numbers are those that can only be divided by themselves and 1 without leaving a remainder. Non-prime numbers are called composite numbers, incidentally.

Turns out that 2016 is not only a composite number but a very composite number! It has a whole eight divisors. Grab a calculator your smartphone and test it for yourself:
2016 = 2 * 2 * 2 * 2 * 2 * 3 * 3 * 7

Whoah! Even the quantity of divisors is anything but simple, since 8 = 2 * 2 * 2.

So what about other years? Was 1917, the year of the Russian Revolution, a ‘prime’ year, for example? No, it wasn’t. 1917 = 3 * 3 * 3 * 71. Just four divisors, but they’re kinda poignant – and prophetic of nothing much good.

So what about other very prime/simple years, and other very non-prime/non-simple ones? Ok, let’s narrow this down a bit to 1980 through present day…

Prime/simple years:

And in the near future there are a few more prime/simples:

(eek, that’s a lot of non-simple years until then)

The most non-prime/non-simple years were:
1984 = 2 * 2 * 2 * 2 * 2 * 2 * 31 (seven divisors)
2000 = 2 * 2 * 2 * 2 * 5 * 5 * 5   (also seven)

There were six divisors in 1980, and there’ll be six in 2025. All other years can be called semi-prime/semi-simple.

But I digress…

Now, in the popular British mathematical journal The Guardian :), readers were recently teased with a… brain teaser. In the blanks between the sequence of figures 10 9 8 7 6 5 4 3 2 1 you need to add arithmetic symbols (+, -, x, ÷, (),) – as many as you like – so as to get the number (year) 2017.

For example, if you add arithmetic signs as follows you get 817:
10 * 9 * (8 + 7 – 6) * (5 – 4) + 3 * 2 + 1 = 817

But how do you add arithmetic to get 2017?
10?9?8?7?6?5?4?3?2?1 = 2017

Come on, have a go!

As for me, in nine minutes I got the equation to equal 2017 by kinda wonky arithmetic (I made the ‘3’ and ‘2’ = ’32’!); then, in around 15 or 20 minutes I got the answer in a proper way without bending the rules. I say ‘a’ way: there are different ways of getting to 2017!

So, tried it yet?

Ok, let’s make it harder: Now take away the 10:
9  8  7  6  5  4  3  2  1 = 2017

Read on: How to make 2017 out of 1?…

Happy New Year from Central Moscow!

Happy New Year folks, and hope you all had great holidays!

You won’t believe this… but this post is about… RED SQUARE! // Incidentally, the square I consider to be the most beautiful spot in Europe!

I hadn’t been in downtown Moscow on New Year’s Eve since… oooh, 15 years ago! Yep – 2001 was the last time, on Pushkin Square watching the fireworks. But I’d never been on Red Square on New Year’s Eve. What?! So this year I decided to make amends…

So how was it? Well, actually, my overall impressions were… mixed. And it’s those mixed impressions that I’d like to share with you today.

Read on: Red Square was really something!…

The Vatican: A Pope’s-Eye View.

Rome. Without a doubt – one of the most… significant cities in the world; 100% must-see. I’ve been to the city many times, toured the different parts of the center on foot several times, prodded, tasted, tried on, and took lots of pics of practically everything. And ‘practically everything’ of course includes St. Peter’s Square, including pics from the top of the dome of St. Peter’s Basilica, taken on three or four separate occasions. But this was the first time I viewed the square from this angle:

And seeing this person in the flesh – that was also a first!

Read on: Palm trees and monuments…

Three Gorgeous Gorges of Energy.

Let’s continue the electricity theme…

Actually, more specifically, in this post it’s a hydroelectric theme; more specifically about a hydroelectric power station; more specifically – the largest hydroelectric power plant in the world. It’s so gigantic you can stare at it for hours, hypnotized: massive majestic concrete walls, vast open spaces… extraordinary in the extreme. And the best bit is the flowing water – which acts as a magnet for the attention of Homo Sapiens.

It’s called the Three Gorges Dam. It’s around 30km from the city of Yichang, and around 300km – or 2½ hours on a train – to the west of Wuhan.

A dam more than two kilometers (2300m!) long, 180 meters high, with a width of the dam wall at the top of 50 meters, and at the base – 120m (as we were told by the girl who was our excursion guide for the afternoon). I mean – just how much concrete was needed for all that?! Oh my gorges.

Read on: More crazy numbers…


Ready? Rant begins – NOW!…

After the Chinese Rail Non-Fail the day before, I could not berliiieeeeeeeve the total fail in a Chinese airport the next day. And not just any old Chinese airport, but the main international airport of China’s capital, no less! The fail was an Internet fail, folks. And the fail was catastrophically, categorically total.

Now, the airport’s immense, beautiful, and just super all round (despite the inevitable Chinese petty tortures/mess-ups), with all its stores, escalators, fountains, sculptures… everything done contemporarily, tastefully and expensively. Everything great except for one thing: no proper Internet! Even mobile Internet ain’t happening, even with a foreign SIM, i.e., with a foreign (not Chinese) number, which doesn’t fall under the Great (Fire)Wall of China. I mean, there is some signal but it’s so weak you might as well not bother.

And I wanted to connect to my blog to write a few ‘on the road’ notes as I like to do, or some ruminations on matters of great importance, plus upload some photos as I like to do, but no – it wasn’t to be. What’s the Chinese for ‘Where’s the Internet, dammit?!’ Please let me know someone. I’ll have it printed on a t-shirt and wear it next time I’m there.

And the ruminations on matters of great importance this week were as follows:

Let’s talk about something that’s so essential to everything that, well, everything – or at least a great many things – wouldn’t exist or be possible. Something so vital that without it life would lose much of its meaning and would become unbearably dull and sad. Something that forms the basis of almost all our modern activities, without which all noble intentions, the reaching of worthy goals, and the securing of a reasonable amount of happiness of various calibers – everything! – would not be possible.

You guessed it yet?

Yep: electricity! What did you think I meant? (Answers > the comments; and keep it clean!)

Just imagine for one minute what would happen if all of a sudden there’d be no more electrical current coming through the sockets – forever! I mean, really: no more, finito, kaput, for ever more!

It would be bad, of course. Real bad. But it wouldn’t be apocalyptic, quite. Life would go on; only – by candlelight and be horse-drawn and with sails!


What’s the name of that sci-fi flick where unfriendly invisible aliens that live on electricity land on earth? Who then consume all the electrons in all the cables and even in natural phenomena like thunderstorms? Where at the end the protagonist, by the light of a candle, bemoans how the thunder’s pealing and the rain’s pouring down but there’s no lightning, and probably never will be?

Update/PS: Further to my emotional rant regarding Beijing’s main airport, a few pics for your viewing pleasure (I finally reached a country that provides good Internet; imagine?! So radically technologically progressive!!).

And here’s pic I took from the plane: morning dead calm, and a column of smoke (or steam) rising up from the middle of a cloud.

That’s all for today folks; back tomorrow…

Greenland, pt. 2 – Airports.

Kangerlussuaq. Probably the strangest international airport in the world. First off, try pronouncing it properly. Hardly slips off the tongue now does it? I had trouble with it too.

Next there’s its geographic and demographic strangeness…

Have you ever seen an international hub airport with a local population of just 500 folks? Not 500,000 – 500! Well, now I have :).

And have you ever seen an airport where for domestic flights there are no security checks whatsoever?! In you stroll, you check in, hand over your luggage, and then you can go walkabout – wherever, including back outside the airport! When your plane’s due you walk to it from wherever you are with no security hassle. A dream!

Ok. Here’s the answer to question No. 2:

Greenland is a very rocky country, and a very glacial one. So building an airport – where you need a good stretch of flat land for the runway itself plus no rockiness in the near vicinity to get in the way of airplanes’ coming in to land and taking off – is no easy task. They did find one spot however that was deemed suitable – Kangerlussuaq: a freak bit of flat bedrock sufficiently far away from the nearest cliffs. The only problem: the runway is a mere 2.8km long!

Read on: Nuuk and Ilulissat

Welcome to Greenland!

By some quirk of fate I often fly across the North Atlantic. Europe-America-Europe; sometimes Asia-America-Europe; sometimes other, more exotic combinations. Example: sometimes I get to fly over Greenland. Sometimes this is at night – so nothing to report there. Other times it’s by day, but the weather’s typically polar and the visibility’s poor. But just sometimes, very occasionally, I get lucky: jetting over Greenland when it’s sunny and panoramic…

One such time for example was in July 2012: Crazy trip, crazy plane, crazy nice weather.


Fast forward to July 2016, and it’s crazy nice weather again up over the big green white land. But this time I wasn’t just flying over, I was to land and then stay a few days. Hurray!

Read on: inside, deeper, more and more …

S. America to S.E. Asia Air-Route Question.

Getting from Cancun in Mexico to Sanya in China, will never be one of the simplest routes – even given the most favorable of weather conditions. All the same, it will never be one of the longest. Still, that route does belong to the category of the ‘trickiest air routes in the world’, i.e., between South America and Southeast Asia (flying in either direction) : the distances are always big, and the air routes are rarely straightforward.

For example, flying from Hong Kong, Bangkok or Kuala Lumpur to Santiago or Buenos Aires will always be an avia-endurance test both in terms of total journey time and the number of connections. I say always, since all available routes – all four of them – all take approximately the same number of hours to complete.

My question:

What are these four (very different) ways of flying (on a commercial flight) from Southeast Asia to South America? (incidentally, one of them I’ve yet to fly myself). Let’s say, from Hong Kong to Santiago and from Hong Kong to Buenos Aires?

World MapSource

Read on: … and the answer is…