Question 3: Number cruncher
Find the next number in the following series:
123, 354, 897, 1875, 10626, __ , ...
Answer: Back to the maths this week with this teaser, which proved a challenge for all bar a select group. The answer is 16887, as expertly worked out (see Solutions below) by: John Bowen, consultant, Bromsgrove, UK; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Sudi Sudarshan, strategic market & technology insights lead, Bridgestone Americas Inc. USA; Michele Girardi, quality manager, Scame Mastaf SpA, Suisio, Italy; David Mann, key account manager, SPC Rubber Compounding, UK:. Very well done to all above, and everyone else who had a go.
The next number is 16887
To get each successive number, move the first digit to the last of each pair, then add the first one to the sum of these two as 231 + 543 + 123 = 897 and so on. [A bit obscure for a Monday morning I think!]
The first digit of the first number is moved to the end, so that 123 becomes 231.
Add these together gives the next number 354.
Continuing this process gives 10626 + 6261 = 16887.
Making a table of the difference with the previous, one can note that it is obtainable by the previous
translating the digits to the left, putting the leftmost at the end , for example 354-123 = 231 , or 354 = 123+231 .
Going on, 897 = 354+543 , 1875 = 897+978 etc . The next number will be 10626+6261 = 16887
Rule: Each subsequent number is derived by adding to the prior number the number obtained by shifting the first digit to the end and shifting positions of the other digits to the left
1st Number: 123
2nd Number = 123 + 231 = 354
3rd Number = 354 + 543 = 897
4th Number = 897 + 978 = 1875
5th Number = 1875 + 8751 = 10626
6th Number = 10626 + 06261 = 16887 (since first digit is 0, it is ignored)
After a few minutes with pencil and calculator; Take the first digit and put it at the end:
123 => 231
Add the two together = 354
And so on until
10626 + 06261 = 16887
Please note: Due to holiday, the next Brainteaser question - and Brainiac of the Month announcement - will be on Monday 2 October.
Question 2: Famous five
What do Carl XVI, Churchill, Elizabeth II , Hillary and Lincoln currently have in common?
Answer: Despite a subtle clue in the title, this teaser worked out quite chewy for many – but not John Coleman, membership manager, Circol ELT, Dublin, Ireland and David Mann, key account manager, SPC Rubber Compounding, UK: both identifying, before any (other) clues were issued, that these people feature on five denomination banknotes in their countries, or coin in the case of King Carl XVI Gustaf. Correct replies followed soon after from: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Sudi Sudarshan, strategic market & technology insights lead, Bridgestone Americas Inc. USA; Michele Girardi, quality manager, Scame Mastaf SpA, Suisio, Italy; John Bowen, consultant, Bromsgrove, UK; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria. Very well done to all above, and everyone else who had a go.
Question 1: A sense of place
Which city, country or other placename might start this series?
____, City of London, Arlington, France,
Answer: As we thought, Bermuda (Triangle) was a go-to answer to this teaser. But not for everyone, with Bolivia, Bosnia and Herzegovina, Mauritania, Namibia, Nicaragua, Rotterdam and even the Raleigh-Durham-Chapel Hill area also showing up in the replies (see ingenious Solutions below). Indeed, we were left half-expecting someone to chip in Switzerland, home of the Toblerone. Anyway, very well done to: John Coleman, membership manager, Circol ELT, Dublin, Ireland; David Mann, key account manager, SPC Rubber Compounding, UK; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; Michele Girardi, quality manager, Scame Mastaf SpA, Suisio, Italy; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; John Bowen, consultant, Bromsgrove, UK; Jose Padron, laboratory analyst, Toyoda Gosei, Waterville, QC, Canada; Sudi Sudarshan, strategic market & technology insights lead, Bridgestone Americas Inc. USA.
Thanks to the Polygon clue the connection between the following places becomes evident:
- City of London – Also known as the Square Mile.
- Arlington, VA – Known for the Pentagon.
- France – often referred to as l'Hexagone.
It then becomes obvious that we are looking for any placename associated with a triangle.
Therefore, the Bermuda Triangle is a suitable fit.
As they have nicknames relating to shapes with increasing numbers of sides (the square mile, the pentagon located in Arlington, l’hexagone..) the logical precedent would be Bermuda (triangle).
The answer could be Nicaragua, because of its triangle shape.
City of London also known as square mile
Arlington home of the Pentagon
France also known as Hexagone
Bosnia and Herzegovina as well as Namibia would also fit.
The first name could be Bermuda, since it's known for its triangle, and :
- London is known for its squares ( Hyde Park, Trafalgar, Kensington , .. )
- the Pentagon is located in Arlington
- The French people refer to their country as the Hexagon
I must admit I wasn’t aware that The Pentagon was in Arlington County, Virginia. Nor would I personally associate the City of London with the term “The Square Mile”.
Due to the shape of the outline of the country of France I understand it is often referred to as “l’Hexagone”. So the answer will be Triangle, with the obvious association of Bermuda as a place name.
First one might be Rotterdam, as it is based on a triangular plan.
London - square mile, Arlington Pentagon, France hexagon.
Well, it seems that this a multiple-answer question, great challenge, looking for countries, cities or other place names with a relation with polygons.
I am just taking countries to answer this brainteaser.
As the City London is well known as the Square Mile
In Arlington County, US is located the Pentagon, the headquarters of US Department of Defense
France is known as the Hexagon because the outline in Europe.
To start this list, it is mandatory to find a 3-sided polygon, a triangle.
The most triangular country is Nicaragua, however there are some other countries with triangular outline; the list includes: Bosnia and Herzegovina, Namibia, Mauritania and Bolivia.
So, I will send my answer with Nicaragua, despite there will be more answers as I noted before.
The Raleigh-Durham-Chapel Hill area of North Carolina, ISA, commonly referred to as The Research Triangle. The clues suggest a sequence of places associated with polygons of increasing number of sides. London, with 'The Square Mile' (4), Arlington with the Pentagon (5) and France with Hexagon (6). So the previous place is associated with a triangle, a polygon with 3 sides. Multiple answers are possible, one of which is The Research Triangle.