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
