ERJ Brainteaser: October 2019

We have a clear winner for our top award this month. For coming up so quickly with the correct answer to uber-tough Question 5 and even finding a mathematical correlation between the figures – a new algorithm for predicting sporting success, perhaps – huge congratulations go to: Michele Girardi of Scame Mastaf our new Brainiac of the Month. 
 

Question 5: Fast figures

If 42 (rounded up to a full whole number) is 7299 (or maybe 7180) and 1.6 is 223 (again rounded up), what is 0.1?
Clues given during the week were: More about sports than a maths question... Time and distance... Record breakers... Go the extra mile...

Answer: A very tricky question, made even more difficult by a blip with 1.6 being incorrectly keyed in as 1.5 – apologies for the error. Despite the hurdles, a select band of readers made it to the finishing line: correctly working out the answer as 10 (9.58s) by identifying that these were the official world record times in seconds for the men’s marathon, mile and 100 metres. Extra well done, so, to: Michele Girardi, Scame Mastaf Spa, Suisio, Italy; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; France Veillette, chef environnement, Usine de Joliette, Bridgestone Canada Inc., Canada: Jose Padron, material development specialist, Waterville TG Inc., Waterville, Québec, Canada; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; Yuichi (Joe) Sano, Sumitomo Electric Industries Ltd, Itami, Japan; John Bowen, consultant, Bromsgrove, UK; David Mann, polymer business development / language coach, Arras, France. Many thanks to everyone else who had a go.

Question 4: What's another year?

Find the missing year:

2017, 2027, 2029, 20XX, 2053

Answer: These are years of prime numbers, so the missing year is 2039. One of those easy-if-know-how questions, otherwise it could take quite some time to work out. Very well done, in order of correct reply, to: Yuichi (Joe) Sano, Sumitomo Electric Industries Ltd, Itami, Japan; John Bowen, consultant, Bromsgrove, UK: Michele Girardi, Scame Mastaf Spa, Suisio, Italy; Fariha Rashid, marketing analyst, Kraton Polymers LLC, Houston, Texas, USA; Paul Knutson, textile engineer, Timken Belts, Springfield, Missouri, USA; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; David Mann, polymer business development / language coach, Arras, France: Mark Bussy, M. Rothschild Co. (NR shipper's agent and broker), domiciled in Spring Lake Heights, New Jersey, USA.

 

Question 3: Five-digit number

How many five-digit numbers are there that do not contain the numbers 3 and 5, and are multiples of 4?

(It cannot start with 0, ie. 01234 is not a 5 digit number)

Answer: When it’s all boiled down, the answer works out neatly as 7 x 8 x 8 x 21 = 9408. Well done, in order of reply, to: Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; John Bowen, consultant, Bromsgrove, UK; Michele Girardi, Scame Mastaf Spa, Suisio, Italy; France Veillette, chef environnement, Usine de Joliette, Bridgestone Canada Inc., Canada: Yuichi (Joe) Sano, Sumitomo Electric Industries Ltd, Itami, Japan; Bharat B Sharma, Sr VP Product Development & Technical Service (Elastomers), Reliance Industries Ltd, Vadodara, Gujarat, India; Jose Padron, material development specialist, Waterville TG Inc., Waterville, Québec, Canada; David Mann, Polymer Business Development, France;

John Bowen’s solution

The rule of divisibility says that a number is a multiple of 4 if its last 2 numbers are multiples of 4. So the last 2 numbers can be 21 different options:00, 04, 08, 12, 16, 20, 24, 28, 40, 44, 48, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96 because they are multiples of 4 and do not have 3's or 5's.

We have the last 2 digits we need to know how many can be in the first digit: 1, 2, 4, 6, 7, 8, 9 and the second and third numbers can have these 7 and number 0 too.

By using permutations we give the possible numbers in each digit and the last 2 digits together.

1st*2nd*3rd*(4th and 5th)=  7x8x8x21
9408

Michele Girardi

A number is divisible by 4 if the number formed by the last 2 digits is .

These are 25 numbers : 00,  04, 08, ..., 96 of these , 4 contain 3 or 5 : 32, 36, 52, 56

So the number of available numbers for the last 2 digits is 25-4=21

The first digit can be 1,2,4,6,7,8,9  ( 7 numbers) the second and third digit can be 0,1,2,4,6,7,8,9 (8 numbers)

The total possibilities are   7 x 8 x 8 x 21 = 9408

France Veillette

To be divisible by 4 a number has to end by 2 digits divisible by 4.  That is 21 possibilities, from 00 to 96, excluding the ones containing a 3 or a 5.  The number of combinations for the first 3 digits, as it cannot start by zero and 3 and 5 are excluded, is 7*8*8=448.  Then 448*21=9408.

Question 2: Grandfather clock

A grandfather works out that his grandson is about as old in days as his son is in weeks. The grandson is also as many months old as the grandfather is in years. If the three together are 140 years old, how old is the grandfather?

Answer: This week’s teaser proved an interesting challenge for many readers with even one or two of our top Brainiacs needing a couple of tries to work out:  the grandfather is 84 years old (his son 49 and grandson 7). 

Well done to the following  readers and everyone else who had a go: Stephan Paischer, head of product management and market intelligence, Semperit AG Holding, Vienna, Austria; John Bowen, consultant, Bromsgrove, UK; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; France Veillette, chef environnement, Usine de Joliette, Bridgestone Canada Inc., Canada; Fariha Rashid, marketing analyst, Kraton Polymers LLC, Houston, Texas, USA; John D Burrows, textile consultant, France; Marc Favre, Camso (no details supplied); Jose Padron, material development specialist, Waterville TG Inc., Waterville, Québec, Canada; Thierry Montcalm, R&D and innovation manager, Soucy Techno, Canada; Paul Knutson, textile engineer, Timken Belts, Springfield, Missouri, USA; Chrystelle Tandonnet, materials & process expert, application & technology development (and innovation team), KSB SAS, Gradignan, France; Michele Girardi, Scame Mastaf SpA, Suisio, Italy; Yuichi (Joe) Sano, Sumitomo Electric Industries Ltd, Itami, Japan; Alan Jackson (no details supplied).

To show how it could be done, here are some of the solutions sent in:

Andrew Knox

If their ages in years are G (grandfather) S (son) and g (grandson)

We know:

1) G + S + g = 140

2) S = 7g

3) G = 12g

Substituting in equation 1): 12g + 7g + g = 140, so g = 7

Substituting in equation 3): G = 12g, so G = 84

(For the age of the son: Substituting in equation 2): S = 7g, so S = 49)

Fariha Rashid

X = grandson, y = son, z = grandfather (ages in years)

X + y + z = 140

365*x = 52*y -> y = 7*x

12*x = z 

X + 7*x + 12*x = 140 -> x = 7, y = 49, z = 84 

Thierry Montcalm

If x is the age in years of the grandfather, y the age in year of the son and z the age in year of the grandson.

We have 365z=52y (or y=365/52 z), 12z=x (ou x=12z) and x+y+z=140.

Replacing x by 12z and y by 365/52 z we have 12z+365/52 z+z=140 or z=7.

If z = 7 and 12z=x then x=84; and y = 365/52 z then y = 49.

The grandfather is 84 years old (the son 49 years old and the grandson 7 years old).

Michele Girardi

Let's indicate them as x,y,z in days

It's

y/7=z

z/(365/12)=x/365

x+y+z=140*365

y=7z

x=12z

z=z

7z+12z+z=140*365

z=7*365   days= 7 years

Substituting we get

49 years and 84 years
 

Question 1: Common number

What do these numbers have in common?

484, 676, 10201, 12321

Answer: The numbers are both squares and palindromes (the same forward and backward).

Bonus question: 

What occurs once in a minute, twice in a moment, but never in a thousand years?

Answer: The letter “m”

 

Few problems for our ‘ace’ brainiacs this week, so well done to: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; John D Burrows, textile consultant, France; John Bowen, consultant, Bromsgrove, UK: Yoganand Nannapaneni, Mascot Systems Private Ltd, Mumbai, India; Yuichi (Joe) Sano, Sumitomo Electric Industries Ltd, Itami, Japan; Bharat B Sharma, Sr VP Product Development & Technical Service (Elastomers), Reliance Industries Ltd, Vadodara, Gujarat, India; Amparo Botella, Ismael Quesada SA, Spain; Michele Girardi, Scame Mastaf Spa, Suisio, Italy; France Veillette, chef environnement, Usine de Joliette, Bridgestone Canada Inc., Canada: Fariha Rashid, marketing analyst, Kraton Polymers LLC, Houston, Texas, USA; Jose Padron, material development specialist, Waterville TG Inc., Waterville, Québec, Canada; Thierry Montcalm, R&D and innovation manager, Soucy Techno, Canada; Ramasubramanian P, manager, marketing – mixer and LTKMPL products, rubber processing machinery, Larsen & Toubro Ltd, Vedal Village,  Kanchipuram, Tamil Nadu, India; Paul Knutson, textile engineer, Timken Belts, Springfield, Missouri, USA; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; Ashley Fahey, sustainability principal vice president, Goodyear Pride Network, Goodyear Tire & Rubber Co., Akron, Ohio, USA.