# ERJ Brainteaser: February

1 Feb 2021

For their neat solutions to tricky Q2, it's well done to **France Veillette** of Bridgestone Canada, **Andrew Knox**, Rubbond Int; **Michele Girardi**, Scame Mastaf and **David Mann**, SPC, the new joint holders of our **Brainiac of the Month** title.

What comes next in the following sequence?

2003, 2011, 2017, 2027, 2029, ___

**Answer**: It did not take sharp-eyed readers that long to identify that this is a sequence of prime numbers, making the next year is 2039. Well done to: **Michael Easton**, director, Globus Group, Trafford Park, Manchester, UK; **Stephan Paischer**, head of product management special products, Semperit AG Holding, Vienna, Austria; **David Mann**, key account manager, SPC Rubber Compounding, UK; **John Bowen**, rubber industry consultant, Bromsgrove, Worcs, UK; **Andrew Knox**, Rubbond International, Ohé en Laak, The Netherlands; **Jose Padron**, material development specialist, Waterville TG Inc., Waterville, Québec, Canada; **France Veillette**: chef environnement, Usine de Joliette, Bridgestone Canada Inc, Canada; **Michele Girardi**, Scame Mastaf Spa, Suisio, Italy; **Federico Fiorini**, managing director, MAI Italia srl, Isola Rizza (VR), Italy.

New, maybe trickier, teaser on Monday.

What should be the value of X in number set B?

A. 7, 11, 14 / 539

B. 6, 9, 21 / X

C. 11, 14, 23 /1,771

**Answer**: 567, ie from the two other number sets, X is the product of the three numbers, divided by 2. Well done to: **Andrew Knox**, Rubbond International, Ohé en Laak, The Netherlands; **Michael Easton**, director, Globus Group, Trafford Park, Manchester, UK; **France Veillette**: chef environnement, Usine de Joliette, Bridgestone Canada Inc, Canada; **Stephan Paischer**, head of product management special products, Semperit AG Holding, Vienna, Austria; **David Mann**, key account manager, SPC Rubber Compounding, UK; **Dominique Cordaillat**, VP industrial purchase, Manufacture Française des Pneumatiques Michelin, Clermont-Ferrand, France; **Federico Fiorini**, managing director, MAI Italia srl, Isola Rizza, Italy; and everyone else who had a go..,.

*Thanks also for the many good wishes after our MBO to acquire European Rubber Journal and start a new chapter in the 136-year history of the magazine.*

New teaser on Monday

Trainspotters Brian A and Brian T stand back-to-back next to a railway line. When the front of a train passes them, Brian A starts walking in the opposite direction of the train, while Brian T walks in the direction of the train.

They walk at exactly the same speed, stopping precisely when the back of the train passes. If Brian A walks exactly 20 metres, and Brian T walks exactly 30 metres, how long is the train?

**Answer**: 120 metres as smartly worked out (see solutions below) by: **France Veillette**: chef environnement, Usine de Joliette, Bridgestone Canada Inc, Canada; **Andrew Knox**, Rubbond International, Ohé en Laak, The Netherlands; **Michele Girardi**, Scame Mastaf Spa, Suisio, Italy; **David Mann**, key account manager, SPC Rubber Compounding, UK. Well done to all and everyone else who had a go.

*Solutions*

*France Veillette - Using the end of the train to determine speed relative to the Brians, the train travel 50 meters while the Brians travel 10 meters. Therefore, the speed of the train is 5 times the speed of the Brians. While Brian T travels 30 meters, the train travels 30 meters + its length (L). time = distance/speed, then 30/x = (30+L)/5x. Therefore, the length of the train is 150-30 = 120 meters.*

*Andrew Knox - . If both Brian A and Brian T walk at, say 2 m/s, then it takes Brian A 10 s to walk 20 m and Brian T 15 seconds to walk 30 m. So the rear of the train travels 20 + 30 = 50 metres in the 5 s extra that Brian T has to keep walking after Brian A stops. So the train is travelling at 50/5 = 10 m/s.
From where Brian A and Brian T start from, the train front travels 150 m from the starting point in the 15 seconds it takes for the rear of the train to pass Brian T, who is now 30 m from the starting point in the direction the train is heading. So the length of the train is 150 - 30 = 120 metres..*

*Michele Girardi - Taking the origin in the position of the trainspotters, the equation of motion of the back of the train is X = v*t-L
Where v is the speed and L is the length. If the two people stop at times
t1 and t2, It's
v*t1-L = -20
v*t2-L = 30
summing L and dividing:
t1/t2= (-20+L)/(30+L)
Since the people walk at the same speed, it's
20/t1=30/t2
t1/t2 = 20/30
Combining the two equations we get
20/30= (-20+L)/(30+L) whose solution is 120.*

*David Mann- Let the train length be L.
If we think about how much faster the train is than T, it covers L + 30 metres when T covers 30 metres. So the ratio is (L + 30)/30. For A the ratio is
(L - 20)/20. But as the spotters walk at the same speed then
(L + 30)/30 = (L-20)/20
Multiplying by 60 and solving gives L = 120
Any decent spotters should have been concentrating on the numbers though!*

What do former president Donald Trump, former FBI director Edgar Hoover have in common with cartoon characters Homer Simpson and Elmer Fudd (Bugs Bunny’s hapless hunter)?

**Answer**: With apologies to those readers who are not so familiar with some of these characters, the letter J features in all of their names: Donald J Trump, J Edgar Hoover, Homer J (okay, it is actually ‘Jay’) Simpson and Elmar J Fudd. Well done to: **Andrew Knox**, Rubbond International, Ohé en Laak, The Netherlands; **John Bowen**, rubber industry consultant, Bromsgrove, Worcs, UK; **Stephan Paischer**, head of product management special products, Semperit AG Holding, Vienna, Austria; **David Mann**, key account manager, SPC Rubber Compounding, UK; **France Veillette**: chef environnement, Usine de Joliette, Bridgestone Canada Inc., Canada; and everyone else who had a go.

New teaser on Monday.