ERJ Brainteaser - December
20 Dec 2024
For a run of superb replies, including in Spanish, its big congratulations to Amparo Botella of Ismael Quesada, our December Brainiac of the Month.
Question 3; Spy in capitals
Which city might complete the following series?
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1. Bogota |
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2. London |
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3. Monaco |
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4. Montevideo |
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5. Moscow |
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6. Oslo |
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7. XXXXXXXXX |
Answer: We received a select number of correct replies, though without anyone identifying the cryptic link to the title Spy in capitals. All capitals have two letter ‘O’s and there are seven of them, so the link is James Bond, code named 007. Still, there were some really good angles applied to this this teaser. Very well done to: Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan; John Bowen, consultant, Bromsgrove, UK; Stephan Paischer, head of product management and market intelligence, Semperit AG Holding, Vienna, Austria; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; and everyone else who had a go.
Please note: The winners of the ERJ Brainiac of the Year Awards will be announced 3 Jan 2025.
Wishing everyone a very Happy Christmas and a great New Year!
SOLUTIONS
Amparo Botella
Pending of next clues, the tentative city number 7. Can be Tokio. I can see that all the cities are capitals of countries and the all contain two letter “o” and are named in alphabetical order.
Andrew Knox
These are all capital cities with two “o”’s in the name (signifying a spy’s binoculars perhaps). So Dodoma (Tanzania), Gaborone (Botswana), and many others would fit (Stockholm here perhaps better after Oslo and the alphabetical sequence of the first letter of the name)
Kamila Staszewska
Good morning
The list contains capital cities with two o's in their names.
The last one is a 9-letter name, which can be Stockholm (the capital of Sweden) or Podgorica (the capital of Montenegro, which also has two o’s in name of the country!).
Additionally, Port Louis (the capital of Mauritius) might also fill the gaps if two-part names are allowed.
John Bowen
9-letter capitals include Stockholm [Sweden] and Reykjavik [Iceland]
[Need more clues to be definite!]
These two also are in alphabetical order, as are all the given ones.
Stephan Paischer
All those are capital cities and contain 2 Os, in alphabetical order.
The next position could be Stockholm.
Sudi Sudarshan
My answer: Stockholm
The list contains names of national capitals in alphabetical order, with O as the first and last vowel. I see that capitals that have two Os in their names like Dodoma (Tanzania) and Gaborone (Botswana) were not included in the list as the two Os are not the first and last vowels.
The next capital after Oslo that meets these criteria is Stockholm.
The last capital on the list would be Tokyo.
Next teaser on 6 Jan - with the Brainiac of the Year Awards to be announced on 3 Jan.
Question 2; Driving test
A test car is driven along a straight horizontal track with constant acceleration. There are three check points A, B and C, in that order, on the road, where AB = 22 m and BC = 104 m. The car takes 2 seconds to travel from A to B and 4 seconds to travel from B to C. What is the acceleration of the car, and the speed of the car at the instant it passes A?
Answer: The initial speed = 6 m/sec and rate of acceleration = 5 m/sec/sec. Very well done, in order of reply, to: Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan; Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; John Bowen, consultant, Bromsgrove, UK; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; and everyone else who had a go.
SOLUTIONS
Kamila Staszewska
s=ut+1/2at^2
From A to B (s=22, t=2):
22=u*2+1/2*a*2^2
22=2u+2a
11=u+a
From B to C (s=104, t=4):
104=u(b)*4+1/2*a*4^4
104=4u(b)+8a=4(u(b)+2a)
26=u(b)+2a; u(b)=u+2a
26=u+4a
{11=u+a
{26=u+4a
{u=11-a
{26=11-a+4a
15=3a
a= 5 (m/s^2)
u=11-5= 6 (m/s)
Acceleration of the car is 5m/s^2 and speed of the car at the instant in A point is 6m/s.
John Bowen
This one needs some old school algebra [simultaneous equations] and laws of motion:
Consider the section A to B, Applying the equation s = ut + 1/2.f.tsqd where s = distance, u = initial velocity, f = acceleration [constant here] and t = time
Then 22 = u.2 + 1/2.f.2.2 - Equation 1
Now section A to C:
126 = u.6 + 1/2.f.6.6 - Equation 2
3 x Equation 1 gives us
66 = u.6 + 3/2.f.2.2 - Equation 3
Subtract Eqn 3 from Eqn 2:
60 = 12.f
f = 5 m/sec/sec
Now to calculate initial speed u at Point A:
Substituting again, 22 = u.2 + 1/2.5.2.2
22 = 2.u + 10
u = 6m/sec
In summary, rate of acceleration = 5 m/sec/sec
Initial speed = 6 m/sec
Amparo Botella
Acceleration: a=5 m/s2a=5m/s2
Initial velocity at A: u=6 m/su=6m/s
This result if found by using the equations of uniformly accelerated motion:
s=ut+12at2s=ut+21?at2 (where ss is the displacement, u is the initial velocity, a is the acceleration, and t is time).
v=u+atv=u+at (velocity after time t).
Where:
uu: Initial velocity of the car at point AA.
aa: Constant acceleration of the car.
t1=2 st1?=2s: Time from AA to BB.
t2=4 st2?=4s: Time from BB to CC.
AB=22 mAB=22m: Distance between AA and BB.
BC=104 mBC=104m: Distance between BB and CC.
Using the first equation of motion:
s=ut+12at2s=ut+21?at2
For A to B, s=22s=22, t=2t=2:
22=2u+12a(22)22=2u+21?a(22)22=2u+2a(1)22=2u+2a(1)
The displacement BC is covered in t=4 st=4s, but the total time from A to C is t=6 st=6s. The displacement from A to C is AB+BC=22+104=126 mAB+BC=22+104=126m.
For the motion from A to C, using the same equation:
126=6u+12a(62)126=6u+21?a(62)126=6u+18a(2)126=6u+18a(2)
2u+2a=22?????u+a=11(3)2u+2a=22?u+a=11(3)
6u+18a=126?????u+3a=21(4)6u+18a=126?u+3a=21(4)
(u+3a)−(u+a)=21−11(u+3a)−(u+a)=21−112a=10?????a=5 m/s22a=10?a=5m/s2
Substitute a=5a=5 into Equation:
u+5=11?????u=6 m/su+5=11?u=6m/s
Sudi Sudarshan
My answer: Acceleration = 5 m/s^2, Velocity when the car passes A = 6 m/s
Solution: Let Va be the velocity of test car at A, A the acceleration.
22 = Va*2 + 0.5*A*(2^2)
2Va + 2A = 22
(22+104) = Va*(2+4) + 0.5*A*(2+4)^2
6Va + 18A = 126
Solving the two simultaneous equations
12A = (126-3*22)=60
A = 5
2Va + 2A = 22
2Va = 22 - 2*5 = 12
Va = 6
Andrew Knox
Answer: Acceleration is 5 m/s/s & speed is 6 m/s when car passes point A.
Distance travelled under constant acceleration is: distance = (initial velocity * time) + (1/2 * acceleration * time^2).
So, we have here 22 = vA .2 + 1/2a.4 and 126 = vA.6 + 1/2.a.36, or 11= vA +a and 21 = vA + 3a.
Solving for a we get 2a = 10 or a = 5 m/s/s.
Solving for vA, we get vA = 11 - a = 6 m/s.
New teaser on Monday
Question 1: Football patch
A football is made by sewing together 12 black pentagonal panels and 20 white hexagonal panels. There is a join wherever two panels meet along an edge.How many joins are there?
Answer: Coinciding with the official number of minutes in a game of football (ie soccer), the solution is 90. Bien jugado: Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; John Bowen, consultant, Bromsgrove, UK; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan; Hans-Bernd Luechtefeld, consultant, Germany; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; David Mann, Polymer Business Development consultant, UK; and everyone else who took a shot.
SOLUTIONS
Amparo Botella
Hay 12 paneles pentagonales negros y 20 paneles hexagonales blancos, lo que da un total de:
F=12+20=32 caras.
Cada pentágono tiene 5 lados, y cada hexágono tiene 6 lados. Pero como cada arista es compartida por dos caras, debemos contar cada lado solo una vez.
Total de lados (sin dividir entre dos):L=(12×5)+(20×6)=60+120=180
Total de aristas (dividiendo entre dos):E=L2=1802=90.
Cada pentágono tiene 5 vértices y cada hexágono tiene 6 vértices, pero cada vértice es compartido por tres caras. Entonces, el número total de vértices es:V=(12×5)+(20×6)3=60+1203=1803=60.V=3(12×5)+(20×6)?=360+120?=3180?=60.
El teorema de Euler establece que:
V−E+F=2.
Sustituyendo los valores calculados:
60−90+32=2.
Esto confirma que los cálculos son correctos.
El número de uniones entre paneles es igual al número de aristas, que ya calculamos:
Uniones=E=90.
Por lo tanto, hay 90 uniones en total
Andrew Knox
Answer: 12x5 + 20x6 = 180 sides, so divide by 2 = 90 joins.
John Bowen
There are 12 pentagonal panels so 60 edges, and 20 hexagonal panels so 120 edges here, giving a total of 180 edges... Each join consists of 2 edges, so there are 90 joins of 2 edges.
Hans-Bernd Lüchtefeld
20*6=120 sides on hexagonal patches and 12 * 5 = 60 sides on pentagonal patches totalling 180 sides.
Around each hexagonal side there are 3 other hexagonal sides and 3 pentagonal sides.
That way, two sides of hexagon to hexagon and two sides of hexagon and pentagon are stitched together. >> Total no. of joints are 180/2=9
Kamila Staszewska
The number of edges is 5x12+6x20= 60+ 120 = 180
Each joint is made with two edges therefore 180/2=90 joints.
Sudi Sudarshan
Solution: There are 12 black pentagons with 60 sides in total and 20 white hexagons with 120 sides in all. However, each side of a hexagon is common with a side of another hexagon or a pentagon.
So the total number of common sides or joins = (60+120)/2 = 90
David Mann
There are 12 x 5 edges on the pentagons and 20 x 6 edges on the hexagons. That makes 180 edges in all. As all the edges are used, and 1 join uses 2 edges, that makes 90 joins.
