ERJ Brainteaser: November
21 Nov 2022
For being first with the answer to tricky Q2, our top award this time goes to Andrew Knox of Rubbond Int. and Katharina Gottfried of Arlanxeo, new joint holders of the Brainiac of the Month title
Question 4: Football stars
In total, how many stars are represented on the official national flags of the countries competing at the FIFA Men’s Football World Cup 2022 in Qatar?
Answer: Rather than getting into a heated debate as to whether or not to include the sun as a star – including on Japan’s flag – or the coat of arms on Costa Rica’s flag, let’s just say well played to our World Cup ‘semi-finalists’: John Bowen, rubber industry consultant, Bromsgrove, Worcs, UK; Andrew Knox, Rubbond International, The Netherlands; Michele Girardi, quality manager, Scame Mastaf Spa, Suisio, Italy; Stephan Paischer, head of product management and market intelligence, Semperit AG Holding, Vienna, Austria; and everyone else who had a go.
Solutions
John Bowen
Of the 32 qualifiers, 13 have flags with stars as follows:
Brazil 27
Ecuador 1 [Sun]
Uruguay 1 [Sun]
Ghana 1
Senegal 1
Tunisia 1
Morocco 1
Cameroon 1
USA 50
Australia 6
Costa Rica 8 [7 stars + 1 setting Sun]
Argentina 1 [Sun]
Croatia 2 [Sun]
Total including Sun = 101
Total without Sun = 95
Andrew Knox.
Answer: 94 - assuming that an image or (in the case of Japan) the representation of the sun also can be counted as stars, also those contained in coats of arms, there are 94 stars in total:
USA: 50
Brazil: 27
Australia: 6
Croatia: 2
and one each for:
Senegal, Argentina (sun), Tunisia, Morocco, Japan (representation of the sun), Cameroon, Uruguay, Ghana, Ecuador,
Michele Girardi
Brazil 27
Ghana 1
Senegal 1
Tunisia 1
Morocco 1
Cameroon 1
USA 50
Australia 6
Total 88
Stephan Paischer
The answer is 90.
Senegal 1
USA 50
Tunisia 1
Australia 6
Croatia 2 (very small though)
Morocco 1
Brazil 27
Cameroon 1
Ghana 1
New teaser on Monday.
Question 3 - Number cruncher
169, 196, ? , 256, 289…
Answer: The series comprises the squares of 13, 14, 15, 16, 17, making 225 the missing number. Very well done to: John Bowen, rubber industry consultant, Bromsgrove, Worcs, UK; David Mann, key account manager, SPC Rubber Compounding, UK; Katharina Gottfried, technical manager, Arlanxeo Deutschland GmbH, Köln, Germany; Andrew Knox, Rubbond International, The Netherlands; Stephan Paischer, head of product management and market intelligence, Semperit AG Holding, Vienna, Austria; Veronika Beer, sustainable development, wdk Wirtschaftsverband der deutschen Kautschukindustrie e.V. (German Rubber Manufacturers Association), Frankfurt am Main, Germany: Horacio Miguel Gini, Papma Energia, Argentina; Michele Girardi, quality manager, Scame Mastaf Spa, Suisio, Italy; Jose Padron, laboratory analyst, Toyoda Gosei, Waterville, QC, Canada; France Veillette, chef environnement, Usine de Joliette, Bridgestone Canada Inc., Canada; Eric Habib, innovation special projects manager, FieldTurf, Montreal, Quebec, Canada; and everyone else who had a go.
New teaser on Monday.
Question 2: City connect
Which city might fill the gap in this list?
Kinshasa, Brazzaville
___, Budapest
Vientiane, Phnom Penh
Cairo, Khartoum
Buenos Aires, Montevideo
Answer: This time, seemingly, at least one of our contestants lives and/or works on/near one of the answers. The listed pairs of cities in the question are all capital cities located on the same rivers (Congo, Mekong, Nile, Rio Plata). So, as well as Budapest, Vienna, Bratislava and Belgrade are all on the Danube. Very well done, in order of correct reply, to: Katharina Gottfried, technical manager, Arlanxeo Deutschland GmbH, Köln, Germany; Andrew Knox, Rubbond International, The Netherlands; John Bowen, rubber industry consultant, Bromsgrove, Worcs, UK; Michele Girardi, quality manager, Scame Mastaf Spa, Suisio, Italy; Stephan Paischer, head of product management and market intelligence, Semperit AG Holding, Vienna, Austria; and everyone one else who had a go.
Question 1: Rubber compound
After a small win on the national lottery, rubber technologist Simon decides to leave €6,000 in a bank savings account for five years at a compound interest of x% per year. At the end of five years the investment is worth €8029.35. Find the value of x.
Answer: If there ever was to be a Bank of Brainiac, account deposits would be in safe hands with our experts here, who accurately and promptly calculated the compound interest value at 6% (solutions below). Very well done to: John Bowen, rubber industry consultant, Bromsgrove, Worcs, UK; Michele Girardi, quality manager, Scame Mastaf Spa, Suisio, Italy; Jose Padron, laboratory analyst, Toyoda Gosei, Waterville, QC, Canada; Andrew Knox, Rubbond International, The Netherlands; John D Burrows, France; Bill Collins, Circol ELT, Dublin, Republic of Ireland; and everyone one else who had a go.
Solutions
John Bowen
For compound interest, the amount A from a sum S at the end of time t years at X% is given by
A = S[1 + X] to the power of t
so 8029.35 = 6000[1 + X]pwr5,
1.338225 = [1 + X]pwr5
X = 0.06, or 6%
Jose Padron
Working with the compound interest formula:
R = I * (1+i)n
R = return after period = 8029.35
I = Investment amount = 6000
n = years of investments = 5
and solving for I with my old chap Excel I got:
i = 6.0%
Andrew Knox
(8029. - 6000)/5 = 405.87
405.87/6000 = 0.0676 or ca. 6.8%
As the interest is compounded annually, try 6%:
6000 x 1.06 x 1.06 x 1.06 x 1.06 x 1.06 = 8029.35 So 6% is indeed correct.
John Burrows
So it seems that Simon found a good investment
The annual interest rate is 6%
In fact 6000 x y^5 = 8029.35
Y^5 = 1.338225
Therefore y = 1.06 giving an annual rate of 6%
Michele Girardi
The formula for compounded interest is
FV(future value) = PV (present value )*(1+i)^n
where i is the annual interest and n is the number of years
Applying to our case :
8029.35 = 6000*(1+x)^5
1+x = ( 8029.35/6000)^(1/5) = 1.06
x=0.06
