# ERJ Brainteaser: October

1 Nov 2024

Some great performances all round, but for ramping Q1 up to 'sextillion’ it’s congratulations to **Stephan Paischer** of Semperit our new **Brainiac of the Month**

Question 4: **Tricky trios**

7, 24, 25

6, 8, 10

5, 12, 13

?, ?, ?

**Answer**: Well done to our select group who recognised the hand of Pythagoros here (see Solutions below), making **4, 3, 5** the correct answer: **Amparo Botella**, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; **John Bowen**, consultant, Bromsgrove, UK; **David Mann**, Polymer Business Development consultant, UK; **Andrew Knox**, Rubbond International, Ohé en Laak, The Netherlands; **Kamila Staszewska**, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; **Sudi Sudarshan**, principal consultant, Global Mobility Strategies, USA; **Selahattin Algan**, ?cra Kurulu Üyesi, executive board member, Kekor Kaucuk, Pendik, ?stanbul, Turkey; and everyone else who had a go. Special mention also to **Michele Girardi**, quality manager, Scame Mastaf SpA, Suisio, Italy who was on the right track.

SOLUTIONS

*Amparo Botella*

*The next trio is 4,3,5*

*Base in the Pythagorean triples, a2+b2=c2*

*72+242=252*

*62+82=102*

*52+122=132*

*42+32=52*

*John Bowen*

*These are pythagorean sets - ie the squares of the first two add up to the square of the final one, so the final line is 3,4,5 - [9 +16 = 25]*

*David Mann*

*These look like Pythagorean right angle triangles such that the square of the hypotenuse is equal to the sum of the squares of the other sides, and in decreasing order of size. So the next one would be 3,4,5.*

*Andrew Knox*

*Hmmm - by chance the same answer using Pythagoros, but this time based on right-angled triangles where a2 + b2 = h2.*

*So, here:*

*Answer 4, 3, 5.*

*1st number and 2nd number are the two sides of a triangle at right-angles to eachother and the 3rd number is the hypotenuse.*

*1st number goes down each time by one, so next row is 4,?,?, and the answer is 4, 3, 5 (4squared + 3squared = 5 squared) or 16 + 9 = 25.*

*Kamila Staszewska*

*These are Pythagorean triplets:*

*7^2 + 24^2 = 25^2*

*6^2 + 8^2 = 10^2*

*5^2 + 12^2 = 13^2*

*The line starts with 7, 6, 5, so next one is 4, therefore:*

*4^2+3^2 = 5^2*

*Sudi Sudarshan*

*These trios are pythogorean triples (a,b,c) that satisfy the condition a^2 + b^2 = c^2 representing the two legs and the hypotenuse of a right triangle. The sets shown are in decreasing order of magnitude of the smallest side of the triangles. The next smaller set is (3,4,5) satisfying the condition 3^2 + 4^2 = 5^2.*

New teaser on Monday

Question 3: **All on board**

1, 18, 4, 13, **?**, 10, 15, 2, 17, 3....

**Answer**: Helped by a clue in the title, perhaps, our top Brainiacs recognised this as the sequence of the numbers around a dartboard going clockwise from 20 – making **6** the correct answer. Very well done to: **David Mann**, polymer business development consultant, UK; **John Bowen**, consultant, Bromsgrove, UK; **Kamila Staszewska**, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; **Andrew Knox**, Rubbond International, Ohé en Laak, The Netherlands; **Hans-Bernd Lüchtefeld**, consultant, Germany; and everyone else who had a throw.

New teaser on Monday

Question 2: **On the buses**

It takes two workers 6 hours to clean a bus. How long will it take them if they are joined by an apprentice working 40% as fast?

**Answer**: Well done to the following readers who worked out **5 Hours **as the correct answer: **John Bowen**, consultant, Bromsgrove, UK; **Kamila Staszewska**, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; **Andrew Knox**, Rubbond International, Ohé en Laak, The Netherlands; **Hans-Bernd Lüchtefeld**, consultant, Germany (Welcome back!); **Sudi Sudarshan**, principal consultant, Global Mobility Strategies, USA; and everyone else who had a go.

SOLUTIONS

**John Bowen**

*Initially there is 6 x 2 = 12hours work.*

*The apprentice works at 40% so total input is 2.4 man-hours per hour,*

*So together they will take [12/2.4] = 5 hours to clean the bus.*

**Michele Girardi **

*The answer is 5 hours .*

*Adding to 2 people an apprentice whose output is 0,4 the nominal, we get 2.4 people equivalent .*

*The output is increased by a factor 2.4/2 , the time is decreased by a factor of 2/2.4 , so*

*6h x 2/2,4 = 12/24*10h = 5h*

**Andrew Knox**

*It will take 12/2.4 = 5 hours.*

**Kamila Staszewska**

*2 workers cleaning the bus in 6h = each worker cleans 1/12 of the bus per hour;*

*Apprentice working 40% as fast = 0.4 * 1/12 = 1/30 per hour;*

*All three: 1/12 + 1/12 + 1/30 per hour = 1/5 bus per hour = 1 bus per 5 hours*

**Hans-Bernd Lüchtefeld**

*1 worker (100%) = 12 hr*

*2 workers (200%) = 6 hrs*

*2,4 workers (240%) = 5 hrs*

**Sudi Sudarshan**

*Let W be the output per worker per hour*

*Total work to clean the bus = 6*2W = 12W*

*The apprentice can do 0.4W of work in an hour.*

*With the apprentice, total amount of work completed = 2.4W*

*Total time needed to complete 12W work = 12W/2.4W = 5 Hours.*

Question 1: **Number crunch**

M6, B9, Tr12, ?

**Answer**: Well done to the following select set, who quickly zeroed in (see Solutions below) on **Q15 **as the answer: **Andrew Knox**, Rubbond International, Ohé en Laak, The Netherlands; **Stephan Paischer**, head of product management special products, Semperit AG Holding, Vienna, Austria; **John Bowen**, consultant, Bromsgrove, UK; **Kamila Staszewska**, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; **Sudi Sudarshan**, principal consultant, Global Mobility Strategies, USA, who spotted the ‘non-capital’ Olympic city connection – and everyone else who had a go. An extra special mention to Stephan Paischer for ramping things up to 's*extillion'.*

SOLUTIONS

*Andrew Knox*

*M6, B9, Tr12, ?*

*Answer: Quadr15 (10^15).*

*(10^6, 10^9, 10^12, 10^15).*

**Stephan Paischer**

*The answer is Qa15, Qi18, Sx21…*

*for Quadrillion, Quintillion, Sextillion*

*It’s abbreviations of large numbers followed by the relevant integer figure.*

*John Bowen*

*These refer to successive powers of 10 raised to the power 3:*

*10 to the 6th is a million, M*

*10 to the 9th is Billion, B*

*10 to the 12th is Trillion, Tr*

*so 10 to the 15th is Quadrillion, Qa*

**Kamila Staszewska**

*The answer is Q15.*

*M6 – million –10^6*

*B9 – billion – 10^9*

*Tr12 – trillion – 10^12*

*Q15 – quadrillion – 10^15*

**Sudi Sudarshan**

*My answer to this week's brainteaser: Q15*

*Solution: Members of the series are the abbreviated large number with the number of zeroes in it (in US convention).*

*M6 =million 6 zeros *

*B9 =billion 9 zeros *

*Tr12 =trillion 12 zeroes*

*Q15 = Quadrillion 16 zeros*