*List of Brainteaser questions over the past couple of months, along with the answers and readers supplying correct replies. The number **of correct answers, as well as speed and quality of reply will help decide our Brainiac of the Month. *

**MAY 2019**

Question 3: **Biker Brian-teaser**

On his regular one-mile commute, Brian took three minutes to cycle to work with the wind directly behind him, and returned home in four minutes, cycling against the same wind-force. How long would his journey have taken if there was no wind?

**Answer**: Okay, a little bit open-to-interpretation regarding whether this was one-way or return journey, but this Brian-teaser really got even our best Brainiacs on their ‘thinking bikes’ – as shown by the two examples further below.

Extra well done, so, to all readers who answered either 3.43 minutes (3min 25.7s) or 6.86 minutes (6 min, 51.4s): **John Bowen**, consultant, Bromsgrove, UK; **Michele Girardi**, Scame Mastaf Spa, Suisio, Italy; **Paul Knutson**, textile engineer, Timken Belts, Springfield, Missouri, USA; **Jose Padron**, material development specialist, Waterville TG Inc., Waterville, Québec, Canada; **Ashley Fahey**, sustainability principal vice president, HERO (LGBTQ ERG), Goodyear Tire & Rubber Co., Akron, Ohio, USA; **Bharat B Sharma**, Sr VP Product Development & Technical Service (Elastomers), Reliance Industries Ltd, Vadodara, Gujarat, India; **Ramasubramanian P**, manager, marketing – mixer and LTKMPL products, rubber processing machinery, Larsen & Toubro Ltd, Vedal Village, Tamil Nadu, India.

**Solutions**:

*John Bowen*: With no wind, the time would be 3minutes 25.7seconds.

[Method: Time = distance/speed

Let distance = D, Speed in still air = V and windspeed = W

then With wind speed = V + W, Against wind speed = V – w

Distance is constant, and D = velocity * distabce,

so [V + W]*3 = [V-W]*4, and rearranging, V = 7W, so W = V/7

So with wind, speed = 8V/7, Against wind speed = 6V/7

Time = Distance/Speed, so

3 = D/[8V/7] and 4 = D/[6V-7]

3 = 7D/8V and 4 = 7D/6V

Multiply 3 by 48:

144 = 42D/V

And multiply 4 by 56:

192 = 56D/V

D/V =Time, so when wind is ) and speed is thus V, Time is 144/42 AND 192/56 – both = 3.42857 minutes or 3min 25.7secs]

*Jose Padron*: Brian would take 6.857 minutes (6 min, 51.4 sec.) would have completed his journey without wind.

Speed with the wind; s+s(wind)=1/3 mile/min

Speed against the wind; s-s(wind)=1/4 mile/min and,

Solving these 2 equation for s we have: 2s=1/3+1/4=7/12

thus: s=7/24 mile/min

The whole journey home-work-home is: 2 miles

and the speed with no wind resistance is: 7/24 mile/min

from the equation: t=d/s=(2*24)/7=48/7=6.875 min.

Elapsed time to complete a journey: 6875 min, = 6min. 51.4 sec.

Question 2: **Missing years**

Fill in the missing years in this tricky millennium sequence:

2307, 2417, 2527, 2637, **_**, **_**, **_.**

**Answer**: Not so tricky after all, as correct answers quickly arrived in from around the world. The key is that the total from adding the first two digits (eg 27) and last two digits (eg 47) equals the number formed by the middle two digits (eg 74).

2307, 2417, 2527, 2637, **2747**, **2857**, **2967**

Well done in order of arrival to: **Amparo Botella**, Ismael Quesada SA, Spain; **Bharat B Sharma**, Sr VP product development & technical service (elastomers), Reliance Industries Ltd, Gujarat, India; **Andrew Knox**, Rubbond International, Ohé en Laak, The Netherlands; **Risto Vettenranta**, technical specialist, Ham-Re Oy, Neuvoton, Finland; **John Bowen**, consultant, Bromsgrove, UK: **Michele Girardi**, Scame Mastaf Spa, Suisio, Italy; **Paul Knutson**, textile engineer, Timken Belts, Springfield, Missouri, USA; **Ashley Fahey**, sustainability principal vice president, HERO (LGBTQ ERG), Goodyear Tire & Rubber Co., Akron, Ohio, USA; **Yuichi (Joe) Sano**, Sumitomo Electric Industries Ltd, Itami, Japan; **Ramasubramanian P**, manager, marketing – mixer and LTKMPL products, rubber processing machinery, Larsen & Toubro Ltd, Vedal Village, Kanchipuram, Tamil Nadu, India; **Hans-Bernd Lüchtefeld**, market research & communication manager, PHP Fibers GmbH, Obernburg, Germany.

Question 1: **Plus or minus 100**

Using only a total of 3 symbols and without rearranging the numerals, try to get to a total of 100 by placing + (plus) and – (minus) signs between: 1 2 3 4 5 6 7 8 9

**Answer**: 123 – 45 – 67 + 89 =100

Very well done, in order of reply to:** John Droogan**, advanced polymers and composites, MegaChem (UK) Ltd, Caldicot, Monmouthshire, UK; **Bharat B Sharma**, Sr VP product development & technical service (elastomers), Reliance Industries Ltd, Gujarat, India; **David Mann**, Polymer Business Development, France; **John Bowen**, consultant, Bromsgrove, UK; **Ramasubramanian P**, manager, marketing – mixer and LTKMPL products, rubber processing machinery, Larsen & Toubro Ltd, Vedal Village, Kanchipuram, Tamil Nadu, India; **Yuichi (Joe) Sano**, Sumitomo Electric Industries Ltd, Itami, Japan; **Paul Knutson**, textile engineer, Timken Belts, Springfield, Missouri, USA. **Thierry Montcalm**, R&D and innovation manager, Soucy Techno, Canada; **Jose Padron**, material development specialist, Waterville TG Inc., Waterville, Québec, Canada; **Amparo Botella**, Ismael Quesada SA, Spain; **Andrew Knox**, Rubbond International, Ohé en Laak, The Netherlands; **Hans-Bernd Lüchtefeld**, market research & communication manager, PHP Fibers GmbH, Obernburg, Germany; **Michele Girardi**, Scame Mastaf Spa, Suisio, Italy; **Lars Linnemann**, R&D manager, Genan A/S, Viborg, Denmark

Special mention also to: **Bob Hall**, Sr. director global marketing, Kraton Polymers LLC, Houston, Texas; **Randa Tharwat**, import manager, Nacita Automotive, Cairo, Egypt and **Salah Younis** (no details given) who got there, but by using a couple of extra symbols.

Also thanks to Jose Padron for showing how to work this out using the matrices in this neat table:

**APRIL**

There can be absolutely no dispute about our top performer in April. For showing up first on the grid each time and navigating a tricky set of teasers, particularly Question 4, big congratulations go to:

**John Droogan **of MegaChem (UK) Ltd, our new **Brainiac of the Month**

Question 4: **Mind the gaps**

Fill in the gaps in the following sequence?

_, 4, _; _ 8, 9, 10, _ ; _, 14, 15, 16, _ ; _, _, _, _, _.

**Answer**: The series comprises sets of numbers flanked by prime numbers in ascending order – though some readers got there using a different rationale.

3, 4, 5 7, 8, 9, 10, 11 13, 14, 15, 16, 17 19, 20, 21, 22, 23

*We do try to keep our questions as original and as Google-proof as possible. As a result, solutions are sometimes a bit less straightforward than intended – as was the case this week.*

However, detecting our ‘prime sandwiches’ straight away was **John Droogan**, advanced polymers and composites, MegaChem (UK) Ltd, Caldicot, Monmouthshire, UK. His reply early Tuesday (day 1) was followed a little bit later by **Franz Hochwimmer**, sales & support inspection systems, Micro-Epsilon Messtechnik GmbH & Co. KG, Ortenburg, Germany; **Paul Knutson**, textile engineer, Timken Belts, Springfield, Missouri, USA; **Thierry Montcalm,** R&D and innovation manager, Soucy Techno, Canada; **Jose Padron**, material development specialist, Waterville TG Inc., Waterville, Québec, Canada; **Ramasubramanian P**, manager, marketing – mixer and LTKMPL products, Larsen & Toubro Ltd, Kanchipuram, Tamil Nadu, India; Y**uichi (Joe) Sano**, Sumitomo Electric Industries Ltd, Itami, Japan. *Well done to all, and everyone else who had a go.*

Question 3: **River crossing**

A father, mother and their two children are crossing a river. Their boat can only take one adult or two children at a time. What is the minimum number of journeys needed to take the family of four across the river?

**Answer**: As per the first correct reply in from John Droogan, (see also table below from Jose Padron) it took them 9 journeys.

2 children across > 1 child back > 1 adult across > 1 child back > 2 children across > 1 child back > 1 adult across > 1 child back > (and finally) 2 children across.

Well done to:** John Droogan**, advanced polymers and composites, MegaChem (UK) Ltd, Caldicot, Monmouthshire, UK; **Hans-Bernd Lüchtefeld**, market research & communication manager, PHP Fibers GmbH, Obernburg, Germany; **David Mann**, Polymer Business Development, France; **Andrew Knox**, Rubbond International, Ohé en Laak, The Netherlands; **Bharat B Sharma**, Sr VP Product Development & Technical Service (Elastomers), Reliance Industries Ltd, Vadodara, Gujarat, India; **Michele Girardi**, Scame Mastaf Spa, Suisio, Italy; **John Bowen**, consultant, Bromsgrove, UK; **Jose Padron**, spécialiste en développement de materiaux, Waterville TG Inc., Québec, Canada; **Paul Knutson**, textile engineer, Timken Belts, Springfield, Missouri, USA; **Yuichi (Joe) Sano**, Sumitomo Electric Industries Ltd, Itami, Japan; **Thierry Montcalm**, R&D and innovation manager, Soucy Techno, Canada; **Bob Hall**, senior director global marketing, Kraton Polymers LLC, Houston, Texas, USA.

Question 2: **High five**

Complete the following series

8,485, 8,516, 8,586, 8,611, _.

**Answer**: Apologies to those readers who spent time trying to work this one out as a mathematical series. There was, though, a strong clue in the title, as the figures represent the height above sea level of the world’s five highest mountains. Our answer, so, was 8848m for Mount Everest, known as Sagarmatha in Nepal and Chomolungma in Tibet.

Well done to peak performers:** John Droogan**, advanced polymers and composites, MegaChem (UK) Ltd, Caldicot, Monmouthshire, UK; **Hans-Bernd Lüchtefeld**, market research & communication manager, PHP Fibers GmbH, Obernburg, Germany (thanks for the photo); **David Mann**, Polymer Business Development, France; **Lars Linnemann**, R&D manager, Genan A/S, Viborg, Denmark; **Bharat B Sharma**, Sr VP Product Development & Technical Service (Elastomers), Reliance Industries Ltd, Vadodara, Gujarat, India (thanks for the table); **Jose Padron**, material development specialist, Waterville TG Inc., Waterville, Québec, Canada; **Yuichi (Joe) Sano**, Sumitomo Electric Industries Ltd, Itami, Japan; **Paul Knutson**, textile engineer, Timken Belts, Springfield, Missouri, USA; **John Bowen**, consultant, Bromsgrove, UK.

Question 1: **Next number**

What number comes next in this series?

100, 500, 1, 50, 1000, 5, ???

**Answer**: The series derives from Roman numerals placed in alphabetical order:

C (100), D (500), I (1), L (50), M (1000), V (5) and then our answer X (10).

Congratulations maximus go to:** John Droogan**, advanced polymers and composites, MegaChem (UK) Ltd, Caldicot, Monmouthshire, UK; **Hans-Bernd Lüchtefeld**, market research & communication manager, PHP Fibers GmbH, Obernburg, Germany; **Amparo Botella**, Ismael Quesada SA, Spain; **John Bowen**, consultant, Bromsgrove, UK; **David Mann**, Polymer Business Development, France; **Bharat B Sharma**, Sr VP Product Development & Technical Service (Elastomers), Reliance Industries Ltd, Vadodara, Gujarat, India; **Yuichi (Joe) Sano**, Sumitomo Electric Industries Ltd, Itami, Japan; **Paul Knutson**, textile engineer, Timken Belts, Springfield, Missouri, USA.

**MARCH **

The top prize this month goes to a clear winner and probably our leading specialist in the field of probability. Well earned congratulations go to: **Michele Girardi** of Scame Mastaf Spa in Italy, the new **Brainiac of the Month**.

Question 4: **Degrees of difficulty**

Add the next number to this series?

60, 90, 108, 120, 128.5714*, 135, 140, 144, 147.2727*, _

*(*5th and 9th numbers are rounded to four decimal places)*

**Answer**: Well done to: **David Mann**, Polymer Business Development, France (thanks for the drawing below); **John Droogan**, advanced polymers and composites, MegaChem (UK) Ltd, Caldicot, Monmouthshire, UK; **Bharat B Sharma**, Sr VP Product Development & Technical Service (Elastomers), Reliance Industries Ltd, Vadodara, Gujarat, India; **Hans-Bernd Lüchtefeld**, market research & communication manager, PHP Fibers GmbH, Obernburg, Germany; **Michele Girardi**, Scame Mastaf Spa, Suisio, Italy; **Amparo Botella**, Ismael Quesada SA, Spain; **Ramasubramanian P**, manager, marketing – mixer and LTKMPL products, Larsen & Toubro Ltd, Kanchipuram, Tamil Nadu, India; **Stephan Paischer**, head of product management special products, Semperit AG Holding, Vienna, Austria; **Paul Knutson**, textile engineer, Timken Belts, Springfield, Missouri, USA.

As John Droogan noted, these are the angles inside a dodecagon: so, 10 x 180 / 12 = 150. We also liked Bharat B Sharma’s explanation (below) and similar approaches by Amparo Botella and Ramasubramanian P among others:

Sides Polygon Sum of all angles Interior angle l

3 Triangle 180° 60°

4 Quadrilateral 360° 90°

5 Pentagon 540° 108°

6 Hexagon 720° 120°

7 Heptagon 900° 128.5714…°

8 Octagon 1080° 135°

9 Nonagon 1260° 140°

10 Decagon 1440° 144°

11 Hendecagon 1620° 147.2727…°

12 Dodecagon 1800° 150

**Question 3: Teacher teaser II**

Question: A follow-on from last week’s ‘divisive question, we asked: There are 12 boys and 8 girls in the class. The teacher selects three children from the class at random to answer a question. What is the probability that the teacher chooses at least two boys?

Answer: A lot more clear-cut this week though only four correct answers suggest this type of question is proving a bit tricky for some. So extra well done to probably our best probability expert **Michele Girardi**, Scame Mastaf Spa, Suisio, Italy as well as to **Hans-Bernd Lüchtefeld**, market research & communication manager, PHP Fibers GmbH, Obernburg, Germany, **Bharat B Sharma,** Sr V.P. product development & technical service (elastomers), Reliance Industries Ltd., India and **P Ramasubramaniam** , Larson & Toubro Ltd, India, who provided the following detailed analysis.

**Solution:**

Probability of the teacher choosing at least two boys is the sum of probability of choosing all three boys and probability of choosing 2 boys and 1 girl.

Probability of choosing all 3 boys : P(BBB) = (12/20)*(11/19)*(10/18) = 0.193

Probability of choosing 2 boys and 1 girl: P(BBG,BGB,GBB) = (12/20)*(11/19)*(8/18) + (12/20)*(8/19)*(11/18)+(8/20)*(12/19)*(11/18) = (1056*3 )/6840 = 0.463

Probability of choosing at least 2 boys is : 0.193 + 0.463 = **0.656**

**Using formula:**

P(at least 2 boys in a selection of 3) = (12C2 x 8C1 + 12C3 x 8C0)/20C3

= ((12×11/2) x (8/1) + (12x11x10/6)x1)/(20x19x18/6)

= (528 + 220)/1140 = 748/1140 = **0.656**

Question 2: **Teacher teaser I**

In introducing herself. a new maths teacher tells her class that she has three children, before asking: if at least one of the children is a boy, what is the probability that she has three sons?

**Answer**: There were several different interpretations of this question, but the actual answer is 1/7 (or 14.3%), as all possible ways of the teacher having the three children must be considered – (ie BBB, BBG, BGB, GBB, GBG, GGB, BGG, but not GGG).

Extra well done to Michele Girardi, Scame Mastaf Spa, Suisio, Italy, who was the only one to get the correct answer, neatly explaining: There are 8 possible combinations of children, only one has no boys, and only one has 3 boys. So, the probability is 1/(8-1)

Tougher bonus question: **Dividing time**

If the digits 1 through to 9 are randomly arranged to make a number, what is the probability that that number is divisible by18?

**Answer**: 4/9 or 0.444. Well done to: Michele Girardi, Scame Mastaf Spa, Suisio, Italy; Amparo Botella, Ismael Quesada SA, Spain; Ramasubramanian P, manager, marketing – mixer and LTKMPL products, Larsen & Toubro Ltd, Kanchipuram, Tamil Nadu, India.

Again, Michele Girardi offered a detailed explanation: 18 = 2*3^2, so a number divisible by 18 must be divisible by 2 and 9. Numbers divisible by 2 must terminate by an even number, numbers are divisible by 9 if the sum of their digits is since: 1+2+3+4+5+6+7+8+9 = 45 (= 9×5), all the numbers created by this random arrangement are divisible by 9. Only the ones terminating by 2, 4, 6, 8, are also divisible by 2 and consequently by 18. The probability of this event is 4/9 = 14.3%. Then the total number of permutations is 9!,there are 8! permutations for each of the 4 even final digits, so the probability is 4*8! /9! = 4/9.

Question 1: **Factorial five, plus one**

Complete the following set of factorials:

5! = 5 x 4 x 3 x 2 x 1=120, 4! = 4 × 3 × 2 × 1 = 24; 3! = ?; 2! = ?; 1! = ?; 0! = ?.

**Answer**:

5! = 5 x 4 x 3 x 2 x 1=120; 4! = 4 × 3 × 2 × 1 = 24; 3! = 3 x 2 x 1 = 6; 2! = 2 x 1 = 2; 1! = 1 x 1 = 1; 0! = 1

Well done to all the following readers who avoided tripping over the final step: realising that 0! is not zero:** ****Andrew Beasley**, product analyst, Hankook Tyre UK Ltd, UK; **David Mann**, Polymer Business Development, France; **John Droogan**, advanced polymers and composites, MegaChem (UK) Ltd, Caldicot, Monmouthshire, UK; **Andrew Knox**, Rubbond International, Ohé en Laak, The Netherlands; **France Veillette**, chef environnement, Usine de Joliette, Bridgestone Canada Inc., Canada: **John Bowen**, consultant, Bromsgrove, UK; **Hans-Bernd Lüchtefeld**, market research & communication manager, PHP Fibers GmbH, Obernburg, Germany; **Ramasubramanian P**, L&T Rubber Processing Machinery, India; **Thierry Montcalm**, R&D and innovation manager, Soucy Techno, Canada; **Stephan Paischer**, head of product management special products, Semperit AG Holding, Vienna, Austria.

Among the many neat explanations provided were Andrew Beasley’s concise definition of n! as n! = n*(n-1)! for n > 0 and this longer one from Ramasubramanian P:

*Mathematically, factorial of a positive integer n is the product of all the integers less than or equal to n and greater than or equal to 1. The significance of ‘factorial’ is that it represents the number of ways ‘n’ elements of a set can be distinctly arranged in a sequence. For example, for a set with three elements, say A,B,C the number of ways this set can be distinctly arranged is 6: ABC, ACB, BCA, BAC, CAB, CBA. Similarly, two elements can be arranged in two distinct ways. A single element can be arranged in only one distinct way. And a set with no elements can be arranged in one distinct way, which is again a NULL set. Hence 0! = 1 too.*

**FEBRUARY**

Great to have a first-time winner of our top award and so well deserved for managing an extra tricky series of teasers this month, including Question 1, which seemed to throw so many of our top players. Huge congratulations go to **Ramasubramanian P** of Larsen & Toubro in India, our new **Brainiac of the Month**.

Question 4: **Country file**

Starting in Turkey and moving west across Europe, find the missing city in the following sequence:

Ankara, _, Oslo, Andorra la Vella.

**Answer**: These are the names (in English) of capital cities beginning and ending with the same letter. The missing city, so, was Warsaw.

Expertly well done to:** John Droogan**, advanced polymers and composites, MegaChem (UK) Ltd, Caldicot, Monmouthshire, UK; **Stephan Paischer**, head of product management special products, Semperit AG Holding, Vienna, Austria; **Andrew Knox**, Rubbond International, Ohé en Laak, The Netherlands; **David Mann**, Polymer Business Development, France; **Ramasubramanian P**, L&T Rubber Processing Machinery, Larsen & Toubro Ltd, Tamil Nadu, India. A special mention also to **Michele Girardi** Scame Mastaf Spa, Suisio, Italy for his help in pointing out a slight blip with the question on Monday.

Bonus question: **More soup**

As we had two valid answers for Question 3, we ran this on into this week, asking readers to identify what came next in the ‘officially’ correct sequence ABC, BCE, CEH, EHM, _

**Answer**: HMU came next in the sequence, as David Mann explained: gaps of 5 and 8 according to the Fibonnaci series.

Well done to: **John Droogan**, advanced polymers and composites, MegaChem (UK) Ltd, Caldicot, Monmouthshire, UK; **Stephan Paischer**, head of product management special products, Semperit AG Holding, Vienna, Austria; **Andrew Knox**, Rubbond International, Ohé en Laak, The Netherlands; **David Mann**, Polymer Business Development, France; **Ramasubramanian P**, L&T Rubber Processing Machinery, Larsen & Toubro Ltd, Tamil Nadu, India; **Amparo Botella**, Ismael Quesada SA, Spain. A special mention also to **Hans-Bernd Lüchtefeld** of PHP Fibers GmbH in Germany, who came quite close with his answer (pictured across).

Question 3: **Alphabet soup**

Find what comes next in the following sequence:

ABC, BCE, CEH, _

**Answer**: As sometimes happens, a valid, alternative answer has emerged for this week’s Brainteaser. So well done to the following readers who worked out the ‘officially’ correct sequence: ABC, BCE, CEH, EHM: **John Droogan**, advanced polymers and composites, MegaChem (UK) Ltd, Caldicot, Monmouthshire, UK; **John Bowen**, consultant, Bromsgrove, UK; **Michael Easton**, sales & marketing director, Globus Group, Manchester, UK; **Michele Girardi**, Scame Mastaf Spa, Suisio, Italy;

And, equally well done to readers who provided the alternative valid answer EHL: **Amparo Botella**, Ismael Quesada SA, Spain; **Bharat B Sharma**, Sr V.P. product development & technical service (elastomers), Reliance Industries Ltd, Vadodara Manufacturing Division, Petrochemicals, Vadodara, Gujarat, India; **Thierry Montcalm**, R&D and innovation manager, Soucy Techno, Canada; **Ramasubramanian P**, L&T Rubber Processing Machinery, Larsen & Toubro Ltd, Tamil Nadu, India; **Varun Sureka**, Hartex Rubber Pvt. Ltd, Hyderabad, India.

This sequence was explained concisely by Amparo Botella: ABC, BC(D)E, CE(FG)H, EH(IJK)L

Question 2: **Flight time**

A projectile is fired at a horizontal velocity of 150 metres/second. It hits a target at a horizontal distance of 30 metres. Assuming negligible air resistance effect, what is a) the flight time of the projectile? and b) its vertical displacement?

**Answers**: Well done to the following readers who answered part (a) correctly ie 0.2 seconds: **John Bowen**, consultant, Bromsgrove, UK; **Thierry Montcalm**, R&D and innovation manager, Soucy Techno, Canada; **P. Ramasubramanian**, Larsen & Toubro Ltd, Rubber Processing Machinery, Tamil Nadu, India: **David Mann**, Polymer Business Development, France; **Olaf Mayer-Mader**, Abteilung BA-M, product management and business development PA, Festo AG & Co. KG, Denkendorf, Germany.

And even more well done to those readers who answered the more tricky part (b) correctly ie 0.196 metres (0.2m also accepted): John Bowen; Thierry Montcalm and David Mann.

John Bowen’s solution neatly shows how it’s done:

a] Flight time = 30/150 = 0.2 secs

b] Vertical displacement: we use s = ut + 1/2.f.tsqd = 0 [fired horizontally so no initial vertical component] + 1/2 * 9.8*0.2*0.2 [f = acceleration due to gravity, 9.8m/sec/sec] = 0.196 metres.

Question 1: **City sequence**

Fill in the missing cities in the following sequence:

Reykjavík, _, Oslo** …** Montevideo , _, Wellington.

**Answer**: Just two correct replies, so extra well done to: **P** **Ramasubramanian**, manager, marketing – mixer and LTKMPL products, rubber processing machinery, Larsen & Toubro Ltd, Vedal Village, Kanchipuram, Tamil Nadu, India; and **Yuichi (Joe) Sano**, Sumitomo Electric Industries Ltd, Itami, Japan. Our other Brainiacs really do need to get out more.

As P Ramasubramanian nicely explained: This is a sequence of national capital cities sorted by latitudes. Northernmost national capital is Reykjavic (capital of Iceland @ 64.14 N) and the southernmost national capital is Wellington (capital of New Zealand @ -41.28 S).

So, the sequence is:

Reykjavic – capital of Iceland (64.14 N), **Helsinki** – capital of Finland (60.17 N), Oslo – capital of Norway (59.9 N) … Montevideo – capital of Uruguay (34.88 S), **Canberra** – capital of Australia (35.3 S), Wellington – capital of New Zealand (41.28 S).

**JANUARY**

When the going got tough, Brainiacs around the world really got going, and this month’s award could have gone to three or four top contestants. Both for dealing so expertly with all four questions, I am sure everyone will join in congratulating **JOHN BOWEN**, our first **BRAINIAC OF THE MONTH** for 2019

Question 4: **Next number B**

Find the next number in the following series:

123, 354, 897, 1875, 10626, ?

**Answer**: Many thanks to all our readers who had a go at this one – not everyone got to the correct answer, 16887. Extra well done, so, in order of reply to: **John Droogan**, advanced polymers and composites, MegaChem (UK) Ltd, Caldicot, Monmouthshire, UK; **Hans-Bernd Lüchtefeld**, market research & communication manager, PHP Fibers GmbH, Obernburg, Germany; **Bharat B Sharma**, Sr VP product development & technical service (elastomers), Reliance Industries Ltd, Gujarat, India; **Ramasubramanian P**, manager, marketing – mixer and LTKMPL products, rubber processing machinery, Larsen & Toubro Ltd, Vedal Village, Kanchipuram, Tamil Nadu, India; **Michele Girardi**, Scame Mastaf Spa, Suisio, Italy; **John Bowen**, consultant, Bromsgrove, UK: **Andrew Beasley**, product analyst, Hankook Tyre UK Ltd, UK; **Michael Easton**, sales and marketing director, Globus Group, Manchester, UK; **Amparo Botella**, Ismael Quesada SA, Spain; **Yuichi (Joe) Sano**, Sumitomo Electric Industries Ltd, Itami, Japan.

*Lots of neat workings out, but here’s John Droogan’s reply – within minutes of the Monday send-out – to show how it’s done:*

*123 > 231 then add 123 gives 354*

*354 > 543 then add 345 gives 897*

*897 > 978 then add 897 gives 1875*

*1875 >8751 then add 1875 gives 10626*

*10626 > 06261 then add 10626 gives 16887.*

Question 3:** Football focus**

In tests for the next World Cup, a football is modelled as a particle and air resistance is ignored. A player kicks the ball from a height of 0.6m above the ground, propelling it vertically upwards at a speed of 10.5m/s. From the modelling, what is the greatest height above the ground reached by the ball, and calculate the length of time the ball is more than 2m above the ground.

**Answer**: Said it might get tougher and it did with only three correct replies to this week’s teaser, from: **John Bowen**, consultant, Bromsgrove, UK: **Bharat B Sharma**, Sr VP product development & technical service (elastomers), Reliance Industries Ltd, Gujarat, India; **Paul Knutson**, textile engineer, Timken Belts, Springfield, Missouri, USA. Their workings out of the correct answers **6.22 metres** and **1.86 seconds** are each given below:

**John Bowen**

*This problem uses the basic Laws of Motion:*

*i] To calculate height reached – ie when the ball stops in its vertical trajectory we use*

*v sqd – u sqd = 2fs, where f = acceleration due to gravity [ in this case -9.81m/sec/sec] and s = distance, u = initial velocity, v = final velocity, so*

*0 – 110.25 = -2*9.81*s*

*s = 5.62, so total height = 5.62 + 0.6 = 6.22m*

*ii] to determine the time above 2m we need to solve a quadratic of the form s = ut + 1/2f*t sqd where t = time in seconds; s = 1.4 [as it starts at a height of 0.6m]*

*so 1.4 = 10.5*t – 1/2*9.81*t sqd*

*solving for t gives values of 1.99 and 0.143, so the ball is above 2m height for 1.85 seconds*

*Greatest height above the ground reached by the ball = 6.225m*

*Total time the ball is more than 2m above the ground.= 1.857 Sec. (**gravity considered as 9.8m/sq.second)*

**Bharat B Sharma **

*1 Initial height = 0.6 *

*v2 = u2 + 2as v=0 *

*u=10.5m/s *

*(10.5)2= 2×9.8xs a= (-9.8m/sec2) *

*s= (10.5×10.5/2×9.8 )+0.5 m(Initial height) *

*s=5.625m+0.6m **= 6.225m *

*2. Time require to keep ball above 2 m from ground (upward 2m to 6.225m and return)*

*Distance covered 4.225 m upward and 4.225 m down ward *

*Going up time Final speed = 0, s= 4.225 m, a =-9.8m/sq.sec== *

*Initial speed at 2 m = sq root of 2×9.8×4.225= sq rt of 82.81 m/sec*

* =9.1 m/sec *

*Time taken to trave 4.225 m= (V=u+at) =0=9.1-9.8t) *

* = time = 9.1/9.8= 0.9286 sec *

*Going down = distance covered 4.225m, Initial speed is 0 and a=9.8m/sec2*

*v sqare=u sq+2as u=0, a=9.8m/sq.sec, s=4.225) *

*v sq= 82.81 *

*v 9.1m/sec *

*Time for return journey will also be 0.9286sec *

*Total time the ball will be above 2 meter height =2*0.92857= 1.857 sec.*

**Paul Knutson**

*Greatest height = 6.22 m. Time above 2 m is 1.86s. All derived from formula y=v0*t-.5*g*t^2*

Question 2:** Next number A**

** **Find the next number in the following sequence: 10, 9, 17, 50, 199, _

**Answer**: Clues were offered but not really needed as correct replies rolled in, including Michele Girardi’s a(i+1)=a(i)*i-1 making the sequence: 1,10; 2,9; 3,17; 4,50; 5,199; 6, **994**. Well done in order of reply to: **John Droogan**, advanced polymers and composites, MegaChem (UK) Ltd, Caldicot, Monmouthshire, UK; **Andrew Beasley**, product analyst, Hankook Tyre UK Ltd, UK; **John Bowen**, consultant, Bromsgrove, UK: **Dave Stuckey**, Dow, South Wales, UK; **Hans-Bernd Lüchtefeld**, market research & communication manager, PHP Fibers GmbH, Obernburg, Germany; **Bharat B Sharma**, Sr VP product development & technical service (elastomers), Reliance Industries Ltd, Gujarat, India; **Michele Girardi**, Scame Mastaf Spa, Suisio, Italy; **Michael Easton**, sales and marketing director, Globus Group, Manchester, UK; **Jon Cutler**, materials development manager, Trelleborg Sealing Solutions, Tewkesbury, UK; **Martin Jones**, customer service manager, network logistics & transport, DHL Supply Chain UK; **Amparo Botella**, Ismael Quesada SA, Spain; **Thierry Montcalm, **R&D manager, Soucy Techno Inc., Canada; **Trey Thies**, growth strategist, engineered performance products, Milliken & Co., Spartanburg, South Carolina, USA; **Yuichi (Joe) Sano**, Sumitomo Electric Industries Ltd, Itami, Japan; **David Mann**, manager rubber technology, SI Group, Béthune, France.

Question 1: **Rubber connect**

Find the rubber connection in: England, Peru, Denmark, Malaysia.

**Answer**: A relatively easy one to start the year, as long you were not thrown off track by ‘Malaysia’ – things might get tougher as we go along. Well done to the following readers who identified EPDM in the country names: **David Mann**, manager rubber technology, SI Group, Béthune, France; **Jose Padron**, material development specialist, Waterville TG Inc., Waterville, Québec, Canada; **John Droogan**, advanced polymers and composites, MegaChem (UK) Ltd, Caldicot, Monmouthshire, UK; **Paul Knutson**, textile engineer, Timken Belts, Springfield, Missouri, USA; **John Bowen**, consultant, Bromsgrove, UK: **France Veillette**, chef environnement, usine de Joliette, Bridgestone Canada Inc. Canada; **Thierry Montcalm**, R&D and innovation manager, Soucy Techno, Canada; **Andrew Knox**, Rubbond International, Ohé en Laak, The Netherlands.

Brainteaser Awards and Results 2018