ERJ Brainteaser: April

Sean randomly guesses the result (whether a team wins, loses or draws) of each of the seven matches taking place between the 14 teams in his local football league next Saturday. What is the probability of him getting each result correct?

Answer: Not quite as controversial as the failed breakaway European Super League, but this question did generate considerable dispute. For example, some readers questioned whether ‘result’ should mean the actual score, while others were unconvinced that Sean had so little knowledge of football that he would ‘randomly’ decide the outcome of each game. But, assuming that result (as we later added) means win, lose or draw, and that all three possible outcomes are equally likely, then there is a 1 in 3 chance of predicting each match. With 7 matches, the probability becomes 1 in 2187 (1/3^7) or 0.0457%.

Well done to our ‘players of the match’: Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; John Bowen, rubber industry consultant, Bromsgrove, Worcs, UK; Flemming Vorbeck, purchasing manager commercial, NDI Group A/S, Brørup, Denmark; Stefano Carletti, R&D Indorama Mobility Group, Office address: Glanzstoff Sicrem Spa, Pizzighettone (CR), Italy; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands.

New teaser on Tuesday
 

If A+B = 76 and A-B = 38, what is the value of A/B = ?

Extra time? 

Which four-digit number multiplied by 4 gives the same number in reverse?

Answer(s). The correct answer for the main question was 3 and for the extra one was 2178 x 4 = 8712. (Please see a small selection of the many fine replies just below).

Very well done to: Michael Easton, director, Globus Group, Trafford Park, Manchester, UK; Flemming Vorbeck, purchasing manager commercial, NDI Group A/S, Brørup, Denmark; David Mann, key account manager, SPC Rubber Compounding, UK; Mehmet Koral, C&C Endüstriyel Danışmanlık, Eğitim ve Mümessillik Ltd, Göztepe, Istanbul, Turkey; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; France Veillette, chef environnement, Usine de Joliette, Bridgestone Canada Inc., Canada; Michele Girardi, Scame Mastaf Spa, Suisio, Italy; John Bowen, rubber industry consultant, Bromsgrove, Worcs, UK; T N Dahal, Kankai Rubber industries, Nepal; Stefano Carletti, R&D Indorama Mobility Group, Office address: Glanzstoff Sicrem Spa, Pizzighettone (CR), Italy; Giorgio Marzari, sales director, RDC srl, Bareggio (MI), Italy; Alexandra Poschlep, head of product management sheeting, Semperit Sheetings, Semperit Technische Produkte GmbH, Wimpassing, Austria.

Solutions

Flemming Vorbeck 

If A+B = 76 and A-B = 38
76-38 = 38
38 / 2 = 19 (B)
76 - 19 (B)  = 57 (A)
38 + 19 (B) = 57 (A)
So…
A (57) + B (19) = 76
A (57) - B (19) = 38
Result:
A (57) / B (19) = 3

Mehmet Koral

If  A+B = 76 and A-B = 38, what is the value of A/B = ?
We start by adding the left and right sides of the 2 given equations:
A+B = 76  
A-B  = 38
2A+B-B=114. --->2A=114
A=57.
Then, 
A+B=76
57+B=76  ------> B=76-57=19.
Now, we are ready to calculate the A/B=?
57/19=3 
The answer is 3.

Andrew Knox

Extra time
Bit of trial and error required here, but by process of elimination one can narrow down the possibilities fairly quickly.
I.e. the 1000 series x 4 can never end in a 1, anything above the 2000 series will result in a 5 digit number, so it has to be in the 2000 series.
So to be reversible it has to end in an 8.
Of these possibilities, only the 21X8 and 22X8 series will work, as 23X8 and above will yield a “9“ as the last digit. So, 2178 is found to work after only 7 “trial an error” calculations.

John Bowen

Extra time
1.    Lets say the number is written as ABCD (1000a+100b+10c+d).
2.    Multiplying it by 4, gives you DCBA (1000d+100c+10b+a)
3.    By divisibility of 4, BA is a two-digit number divisible by 4.
4.    Now, the largest possible value of ABCD is 2499, because anything more will result in a five digit number when multiplied by 4.
5.    Out of the two possibilities 1 and 2 for A, [3] follows that A is even, so 2.
6.    From [5], D is either 8 or 9. However, since D times 4 would end in 2, D is 8.
7.    Using [2], 4000a+400b+40c+4d = 1000d+100c+10b+a, which would simplify to 2c-13b = 1 after substituting A = 2 and D = 8.
8.    The only possible value of ABCD is 2178

Alexandra Poschlep

Extra time:
It must be something below 2500 
ABCD = DCBA
From the logic it must be at least A*4 and found out  2 and 8 (as 8:2 = 4) and it must be starting with the low and and with the high fit the best >2000 but <2500.
A = 2
D = 8
2BC8
Then I tried several possibilities and found out that the inner part B and C must be reduced by -1 from the left and from the right 
Therefore, I came to 2178.

Please complete the following:

Norway, Sweden, Burma, Austria, Peru, Egypt, Ghana, South Korea, ___.

Answer: As well as being expert in maths, chemistry, geography, sports and sometimes even lateral thinking, our Brainiacs must, as in this case, also have a sound knowledge of global politics. The series is a list of the countries of origin of the United Nations secretary generals: the current one being Antonio Guterres of Portugal.

Well done, in order of reply, to: Michael Easton, director, Globus Group, Trafford Park, Manchester, UK; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; John Bowen, rubber industry consultant, Bromsgrove, Worcs, UK; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; France Veillette: chef environnement, Usine de Joliette, Bridgestone Canada Inc., Canada; Stefano Carletti, R&D, Indorama Mobility Group. Office address Glanzstoff Sicrem Spa, Pizzighettone (CR), Italy; Michele Girardi, Scame  Mastaf Spa, Suisio, Italy; Mehmet Koral, C&C Endüstriyel Danışmanlık, Eğitim ve Mümessillik Ltd, Göztepe, Istanbul, Turkey.

New teaser on Monday

What should come next in the following series?:

Boron, Nitrogen, Sodium, Aluminium, Chlorine, …

Answer: Not our toughest ever teaser, but not our easiest either. The atomic numbers of these elements give a series of prime numbers, making the next element potassium, which has an atomic number 19. 
Well done to: Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; Francesco Parazzoli, R&D - material development, new raw materials, Pirelli Tyre SpA, Milano, Italy; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Michael Easton, director, Globus Group, Trafford Park, Manchester, UK; John Bowen, rubber industry consultant, Bromsgrove, Worcs, UK; Stefano Carletti, R&D, Indorama Mobility Group. Office address Glanzstoff Sicrem Spa, Pizzighettone (CR), Italy; Michele Girardi, Scame  Mastaf Spa, Suisio, Italy; France Veillette: chef environnement, Usine de Joliette, Bridgestone Canada Inc., Canada; Daniel Willrich, redakteur, büro Köln, AutoRäderReifen-Gummibereifung, Köln, Germany; Jose Padron, material development specialist (many thanks for the illustration), Waterville, Québec, Canada; and everyone else who had a go. We might also flag up Italy as the top country this week, with three correct replies.

New teaser on Monday

Maths expert Matt is studying his 24-hour digital clock, which displays the time in hours and minutes. He decides to work out what proportion of the day does it display at least one '1'. What should Matt’s answer be?

Answer: Readers were left all in a daze by this one except for three top Brainiacs, who worked out the answer as 62.5 %. Extremely well done in order of reply to: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Michele Girardi, Scame  Mastaf Spa, Suisio, Italy; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; and everyone else who had a go. 

Solutions

Andrew Knox
In the 12 hours that do not have a "1" in them, (i.e. 00, 02, 03, 04, 05, 06, 07, 08, 09, 20, 22, 23) there are 15 minutes which do contain a "1", i.e. 01, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, so 12 x 15 = 180 minutes.
In the other 12 hours that do contain a 1, every minute of the hour will contain at least one "1", so 12x60 = 720 minutes.
So, proportion of minutes in 24 hours that contain at least one "1" is (180 + 720)/(24 x 60) = 900/1440 = 62.5%

Michele Girardi
There are 60 numbers for minutes, 15 have one's, 45 not
- there are 24 numbers for hours , 12 have ones, 12 have not
- there are 24*60 = 1440 possible displays in one day
- of these 45*12 = 540 have no ones
- the percentage of displays with at least a one is ( 1440-540)/1440= 62,5%

Stephan Paischer
First digit:         1x:xx                10 hrs (from 10:00 – 19:59)
Second digit:    x1:xx                2 hrs (overall it happens 3 times per day, for 1 hr each, but one hour is already covered by the first digit)
Third digit:        xx:1x                2 hrs (overall it happens 10 mins per hour, but to be considered only for the remaining 12 hrs – so 12 x 10 min = 120 mins)
Fourth digit:      xx:x1                1 hr (overall it happens 1 min every 10 mins, but here to be considered only 5 times for every of the remaining 12 hrs, as 1 from the 6 times is already covered by the third digit, so 5 x 12 = 60 min)
Total 15 hrs, this is 62,5% of 24 hrs.

New teaser on Tuesday