# ERJ Brainteaser; January 2023

27 Jan 2023

We kick off 2023 with some great answering, not least to Q4. Well done, so, to **David Mann** of SPC Rubber Compounding, winner of this year’s first **Brainac of the Month** award

Question 4: **Making a meal of it**

What might fill the gap in this (mixed) sequence?

Eagle, _, Bagel, Breadstick…

*Clues given during the week: Sports terms, Golf, Tennis…*

**Answer**: This week’s teaser, admittedly, required familiarity with sports terms - in the English language (apologies) - but was still no ‘penalty kick’. Very well done to the following readers with an extra special mention to David Mann, who answered before any clues were issued: **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; **Michele Girardi**, quality manager, Scame Mastaf Spa, Suisio, Italy; and everyone else who had a go.

Solutions

*David Mann*

*I think these might be representations of the sequence -2, -1, 0, 1.*

*Eagle; 2 under par*

*Bagel and breadstick: look like 0 and 1*

*So I’ll offer i squared as one possible answer*

*John Bowen*

*How about BIRDY referring in golf to a winning golf score of 1 under*

*Par? [Eagle is from golf - 2 under par for a hole, Bagel from tennis -*

*a set finishing 6-0, Breadstick again from tennis, a set finishing 6-1]*

*Andrew Knox*

*An Eagle in golf is 2 under par (par is the number of shots a good player should take on a particular hole). Eagle therefore equates to -2.*

*A Bagel is a sort of donut, which looks like a zero, and in American slang is used in tennis in the expression "to be bagelled" i.e. to be beaten without scoring (i.e. to lose a set 6-0) Bagel therefore equates to 0.*

*A Breadstick, looking like a one, is also used in tennis in the expression "to be breadsticked" i.e. losing "something to 1" (6-1 for example), so Breadstick equates to 1.*

*So in this sequence, the gap could be filled with "Birdie", which in golf is scoring 1 under par, i.e. -1.*

*The sequence is then -2, -1, 0, 1.*

*Michele Girardi*

*All the terms are colloquial words related to sports:*

*- "eagle"is a golf score that means two strokes under par, which is the number of pre-determined strokes to complete a hole*

*- in tennis, "bagel" means winning or losing a set 6–0 and "breadstick" means winning or losing a set 6–1*

*The missing term should be from golf, closed to "eagle", it could be "birdie" a golf score that means one stroke under par.*

New teaser on Monday

Question 3: **Next year?**

1681, 1764, 1849, 1936, ?

**Answer**: While this teaser was quite straightforward, readers came up with an interesting array of solutions (see below) to get to the correct answer, **2025**. Very well done to: **John Bowen**, rubber industry consultant, Bromsgrove, Worcs, UK; **Andrew Knox**, Rubbond International, The Netherlands; **Amparo Botella**, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; **David Mann**, key account manager, SPC Rubber Compounding, UK; **Michele Girardi**, quality manager, Scame Mastaf Spa, Suisio, Italy; **Jonas Dispersyn**, innovation platform leader – superior tire performance, NV Bekaert SA, Deerlijk, Belgium; **Stephan Paischer**, head of product management and market intelligence, Semperit AG Holding, Vienna, Austria; **Jose Padron**, laboratory analyst, Toyoda Gosei, Waterville, QC, Canada.

Solutions

*John Bowen*

*Next is 2025*

*Intervals are 83,85,87, next is 89, making 2025*

*Andrew Knox*

*Answer: 2025*

*Simple series with delta increasing each time by 2.*

*Amparo Botella*

*For this one, the answer is 2025, as the series is:*

*1681+83= 1764*

*1764+85=1849*

*1849+87=1936*

*1936+89=2025*

*David Mann*

*If the first 2 digits are a sequence 16,17,18,19… and the second 2 are a series of decreasing squares 81,64,48,36..*

*… then the next will be 2025.*

*Michele Girardi*

*The next one could be 2025, since all the others are consecutive squares :*

*1681 = 41^2*

*1764 = 42^2*

*1849 = 43^2*

*1936 = 44^2*

*2025 = 45^2*

*Jonas Dispersyn*

*41^2=1681*

*42^2=1764*

*43^2=1849*

*44^2=1936*

*45^2=2025*

*Next year is 2025*

*Stephan Paischer*

*The figures given are squares of 41, 42, 43 and 44, so the next one is the square of 45 = 2025.*

Jose Padron

New teaser on Monday

Question 2: **BL3**

Over the holiday period, Brian and Lisa devised a three-level party game, with the winner scooping a €10 prize. First, a coin is flipped twice and if Lisa gets both calls correct the game ends with her collecting the prize. If not, then Brian wins the €10 if he correctly guesses the number (1 to 6) from the roll of a dice. If not, Lisa next picks two numbers between 1 and 5. She wins if either number shows on cards, marked 1, 2, 3, 4, 5, when randomly drawn from a box. If not, Brian wins. Who is more likely to win the €10 prize?

**Answer**: This teaser seemed to throw quite a few readers but, as per the solutions below, Brian and Lisa had an equal chance of winning. Very well done to: **John Bowen**, rubber industry consultant, Bromsgrove, Worcs, UK; **Guillaume Jacques**, materials R&D project manager, Aptar Pharma, Val de Reuil, France; **Veronika Beer**, sustainable development, wdk Wirtschaftsverband der deutschen Kautschukindustrie e.V. (German Rubber Manufacturers Association), Frankfurt am Main, Germany; **David Mann**, key account manager, SPC Rubber Compounding, UK; **Tim Clayfield**, Switzerland; and everyone else who had a go.

Solutions

*John Bowen*

*At the first game, Lisa's chance is 1/4, and Brian’s of going forward is 3/4, where his chance of winning is 1/6 x 3/4 = 1/8 in the second game.*

*For the final game, Lisa’s chance of winning having got this far is 2/5 x 5/8 = 1/4, so Lisa’s cumulative chance of winning is 1/4 + 1/4 = 1/2.*

*Brian’s chance of winning the 3rd game is 3/5 so overall is 1/8 + 3/8 = 1/2*

*Guillaume Jacques*

*They should probably just do a one-coin flip challenge!*

*Their test is a draw:*

*Lisa gets 25% from test 1 (1 chance out of 4 on guessing 2 consecutive coin flips).**Brian then gets a 16.7% chance from test 2 (1 chance out of 6), combined with 75% chance of failure from test 1 ==> 12.5%**Then Lisa gets a 40% chance from test 3 (2 chances out of 5), combined with 83.3% from test 2 x 75% from test 1 ==> 25%**Which leaves another 37.5% to Brian (60% from test 3 x 83.3% from test 2 x 75% from test 1)*

*Total is then:*

*25+25 = 50% overall probability for Lisa**12.5 + 37.5 = 50% overall probability for Brian*

*David Mann*

*Round 1*

*Brian 0 probability, Lisa 0.25 probability. In round 2 Brian wins 1 in 6 times, Lisa never, but there’s only 0.75 probability to share, so Brian 0.125 probability, Lisa 0 probability.*

*In the last round there’s 0.625 probability to share and Brian wins 3 out of 5 times, Lisa 2 out of 5.*

*Brian 0.375 probability, Lisa 0.25 probability.*

*Total probability:*

*Brian 0.5, Lisa 0.5*

*They are equally likely to win the prize.*

*Veronica Beer*

Question 1: **Next up?**

…, 1758, 1835, 1910, 1986, ?, …

*Clues: Rocket science?, Rock around the clock…*

**Answer**: Happy New Year to all. Our first teaser of the year is all about Halley’s Comet, next due around in **2061**. Well done to: **John Bowen**, rubber industry consultant, Bromsgrove, Worcs, UK; **Andrew Knox**, Rubbond International, The Netherlands; **Jose Padron**, laboratory analyst, Toyoda Gosei, Waterville, QC, Canada; **Trevor Elison**, manufacturing engineer, Mountville Rubber Co., LaGrange, Georgia, USA; **David Mann**, key account manager, SPC Rubber Compounding, UK; **Mehmet Koral**, Erhardt-Leimer representative for Turkey, managing director, C&C Endüstriyel Dan??manl?k, E?itim ve Mümessillik Ltd, Göztepe, Istanbul, Turkey; **Bruno Van Damme**, Recytyre, Brussels, Belgium; and everyone else who had a go.

New teaser on Monday