ERJ Brainteaser: June
25 May 2020
This month’s top award was decided by some razor-sharp answering for Q2 and Q4. Honours and congratulations, so, are yet again shared: this time between Stephan Paischer of Semperit and Vivian Zhou of Continental Tires – our new joint holders of the Brainiac of the Month title!
Artist Christine paints a 30cm white cube blue on all sides. She then cuts the cube into smaller cubes of dimension 10cm, collects and throws them up so that they land randomly onto the floor. What is the probability that all the top facing surfaces are blue?
Answer: This is as close as we have ever been to a trick question: the probability being zero, as the central cube will remain uncoloured. Not caught out, in order of reply, were: John Bowen, consultant, Bromsgrove, UK: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Michele Girardi, Scame Mastaf Spa, Suisio, Italy; Jose Padron, material development specialist, Waterville TG Inc., Waterville, Québec, Canada; David Mann, key account manager, SPC Rubber Compounding, UK; Daniel Willrich, redakteur, AutoRäderReifen-Gummibereifung, Hannover, Germany; Vivian Zhou, senior business development & market intelligence analyst. BU RE PLT APAC, Continental Tires (Shanghai) Co. Ltd, Shanghai, China; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria.
Solutions:
David Mann: As the cube from the centre of the original cube will be white on all sides, the probability is zero isn’t it? If you flip the question and estimate the probability of them all being white, it’s something like 1.008 x 10^-5. If you toss away the central cube than the probability of all the others being blue is 1.57 x 10^-15.
Jose Padron: The divided cube give 27 small cubes, with 162 faces. There are 54 blue faces: 8 cubes with three painted surfaces; thus, 8*3 = 24 blue sides out of 8*6 = 48 total sides; 12 cubes with two painted surfaces. Thus, 12*2 = 24 blue sides out of 12*6 = 72 total sides
6 cubes with one painted surface; thus, 6*1 = 6 blue sides out of 6*6 = 36 total sides However, there is; one cube with no painted surfaces. The core of the original cube was not painted.
Bonus question:
Unless you are an avid reader of ERJ back issues, it was rather difficult to guess the precise year of the article. Extra well done, so, to Stephan Paischer, Jose Padron, Andrew Knox who came in right on the money with 2014.
Try to guess the year-of-publication of the following snippet from the ERJ archives, which date back to 1884.
Clues given during the week: Look to the sides... Then the central three numbers... 4+10+13...
Answer: You either saw it or – as was the case for most readers – you didn't. Super well done so to Vivian Zhou, senior business development & market intelligence analyst. BU RE PLT APAC, Continental Tires (Shanghai) Co. Ltd, Shanghai, China who came up with the correct answer first thing on Monday ie without any clues. A bit later in the week, Daniel Willrich, redakteur, AutoRäderReifen-Gummibereifung, Hannover, Germany; Paul Knutson, textile engineer, Timken Belts, Springfield, Missouri, USA; and Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; also saw that combining the two digits on the outside left and right columns in each row gave the sum of the figures in the three central squares. Hence 13 + 6 + 20 = 39 etc. Many thanks to everyone who had a go at this week's tricky teaser.
New teaser on Monday...
Can you work out the values for X and Y in the third number triangle shown below?
Answer: Good to see so many readers pick themselves up and dust themselves off after last week’s unintentional bruiser. With X = 196 and Y = 7, these triangles proved not so tricky for (in order of reply): Michael Easton, sales and marketing director, Globus Group, Manchester, UK; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; Liz O’Donovan, sales and admin assistant, Tyremaster, Dublin, Republic of Ireland; John Bowen, consultant, Bromsgrove, UK: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Michele Girardi, Scame Mastaf Spa, Suisio, Italy; Vivian Zhou, senior business development & market intelligence analyst. BU RE PLT APAC, Continental Tires (Shanghai) Co. Ltd, Shanghai, China; Gonzalo J. González, Lagon Rubber S.L., Portal de Gamarra, Vitoria, Spain; France Veillette, chef environnement, Usine de Joliette, Bridgestone Canada Inc., Canada: Jose Padron, material development specialist, Waterville TG Inc., Waterville, Québec, Canada; Katharina Gottfried, technical manager, Arlanxeo Deutschland GmbH, Köln, Germany; David Mann, key account manager, SPC Rubber Compounding, UK; Paul Knutson, textile engineer, Timken Belts, Springfield, Missouri, USA. Well done to all, and everyone else who had a go.
Special mention to David Mann, for this neat mathematical approach: If we call the apex of the triangle A and the right hand base B then by examination
X=BY
A=BX
Solving gives X=196, Y=7
Bonus question
Try to guess the year-of-publication of the following snippet from the ERJ archives, which date back to 1884. As a bit more to go on, it was a notable year for Popeye, Oscars and London phone boxes.....
Answer: The publication date was 29 June 1929. More or less everyone above clocked in with the exact year – some likely helped by those clues.
Many thanks to Jose Padron for this backgrounder:
Popeye character was created on January 17, 1929
The beverage 7-up was launched in 1929,
The first Academy award ceremony was held on May 16, 1929
The London phone boxes for the police use was unveiled in 1929, The Gilbert McKenzie Trench was a blue box.
Fill in the gap:
London, Monaco, Oslo, _, Podgorica, Moscow
Clues during the week: James Bond minus 1, Capitals west-to-east... ABBA.
Answer: A bridge too far even for many of our most experienced Brainiacs. Nevertheless, this week did produce a standout performance from Stephan Paischer, who twigged from the James Bond clue (double ‘O’ 6) that this was a list of six capital city names in Europe containing two ‘O’s. The answer, so, is Stockholm and extremely well done to Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; followed by Michele Girardi, Scame Mastaf Spa, Suisio, Italy; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Jose Padron, material development specialist, Waterville TG Inc., Waterville, Québec, Canada;
Bonus question
Try to guess the year-of-publication of the following snippet from the ERJ archives, which date back to 1884.
Answer: This is just one of many weird and wonderful inventions in our earliest issues, as people tried to find novel applications for rubber. The actual publication date was 8 October 1886, and closest to the mark again was Andrew Knox with 1890.
What comes next in the following sequence;
66, 78, 93, 105, 111, 114, _
Answer: Adding the digits of each number gives the next number, making 120 next in the series. Well done to: Jose Padron, material development specialist, Waterville TG Inc., Waterville, Québec, Canada: David Mann, key account manager, SPC Rubber Compounding, UK: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Michael Easton, sales and marketing director, Globus Group, Manchester, UK; Vivian Zhou, Senior business development & market intelligence analyst, Continental Tires (Shanghai) Co., Shanghai, China.
Bonus question
Try to guess the year-of-publication of the following snippet from the ERJ archives, which date back to 1884.
Our bonus question was tricky, as evidenced by the wide variation in answers; from 1857 to 1988. Closest to the mark was Andrew Knox with 1927, just a few years away from the actual publication date: 12 Dec 1931. Well done to all, as there was no information there to help date the report.
