ERJ Brainteaser: August 2019

Pete’s plane from Melbourne to Canberra leaves at the same time as Don’s plane from Canberra heads toward Melbourne. The wind current is around 5mph and is travelling against the Don’s plane. Both planes are travelling at 120 miles per hour relative to the wind (not the ground). If the distance between the two cities is 300 miles, how long will it take for the two planes to meet?

Answer: Well done to the following readers who gently landed on the correct answer, 75 minutes: Bharat B Sharma, Sr V.P. Product Development & Technical Service (Elastomers), Reliance Industries Ltd, Vadodara, Gujarat, India; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; John Bowen, consultant, Bromsgrove, UK; Paul Knutson, textile engineer, Timken Belts, Springfield, Missouri, USA; John D Burrows, (details not supplied); Fariha Rashid, marketing analyst, Kraton Polymers LLC , Houston, Texas; Hans-Bernd Lüchtefeld, market research & communication manager, PHP Fibers GmbH, Obernburg, Germany; Ramasubramanian P, manager, marketing – mixer and LTKMPL products, rubber processing machinery, Larsen & Toubro Ltd, Vedal Village,  Kanchipuram, Tamil Nadu, India.

As Bharat B Sharma neatly worked out:

1.25 Hours (or 75 minutes)

Both planes speed== 120mph

Dons’ plane speed—120-5mph== 115 mph

Pete’s plane speed – 120+5mph== 125 mph.

Time when both plane will meet

115xt + 125xt = 300 (total distance)

240t=300

T= 1.25 hours (75 minutes)

Frank, a tire enthusiast, has a  collection of various types of tires in his garage. When his wife asked how many tires he had, he replied: “Well! If I divide them into two unequal numbers, then 32 times the difference between the two numbers equals the difference between the squares of the two numbers.” How many tires does Frank have?

Answer: 32. Well done to Hans-Bernd Lüchtefeld, market research & communication manager, PHP Fibers GmbH, Obernburg, Germany. 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; John Bowen, consultant, Bromsgrove, UK; David Mann, Polymer Business Development, France; Paul Knutson, textile engineer, Timken Belts, Springfield, Missouri, USA; France Veillette, chef environnement, Usine de Joliette, Bridgestone Canada Inc., Canada; Ramasubramanian P, manager, marketing – mixer and LTKMPL products, rubber processing machinery, Larsen & Toubro Ltd, Vedal Village,  Kanchipuram, Tamil Nadu, India; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands;  Yoganand Nannapaneni, Mascot Systems Private Ltd, Mumbai, India; John D Burrows.

The formula as provided by John Burrows:

32 (x-y) = (x2 – y2)

32(x-y) = (x+y).(x-y)

So 32 = x+y

If you use a certain formula on 13, you end up with 7. Under the same formula, 2352 becomes 16, 246 becomes 14, 700 turns into 16, and 1030 becomes 14. What would 9304 become?

Answer: Just two readers came up with the answer for this tricky teaser – 19. But never mind the quantity, look at quality of the excellent replies (below) from: Bharat B Sharma, Sr VP Product Development & Technical Service (Elastomers), Reliance Industries Ltd, Vadodara, Gujarat, India; and Hans-Bernd Lüchtefeld, market research & communication manager, PHP Fibers GmbH, Obernburg, Germany. Very well done to both, and many thanks to everyone else who had a go.

Bharat B Sharma:

Hans-Bernd Lüchtefeld

Formula: Convert the number to binary; add 1 for every zero, add 2 for every 1:

Which country comes next in the following list?:

Greece

Netherlands

Belgium

France

(Clues given during the week: It is to do with numbers, codes…)

Answer: It is always good to have a clear winner, and this time around it is a big congratulations to Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands who came up with the correct answer first thing on Monday morning. This related to a numeric sequence of international telephone dial codes in these countries: with Spain next on the list:

Greece 30, Netherlands 31, Belgium 32, France 33, Spain 34

Also ‘ringing in’ with the correct solution – just a little after Andrew –  were: David Mann, Polymer Business Development, France; Yoganand Nannapaneni, Mascot Systems Private Ltd, Mumbai, India; Yuichi (Joe) Sano, Sumitomo Electric Industries Ltd, Itami, Japan; John Bowen, consultant, Bromsgrove, UK; Hans-Bernd Lüchtefeld, market research & communication manager, PHP Fibers GmbH, Obernburg, Germany; Fariha Rashid, marketing analyst, Kraton Polymers LLC, Houston, Texas, USA.  Well done to all and everyone else who had a go – especially those from outside the EU, as this was a slightly Europe-centric question.

Tire technician Simon is trying his hand at blackjack on a two-deck table in Las Vegas. The dealer rolls through 3 hands in which Simon counts 17 face cards and 29 non face cards. On the fourth hand he sees 4 face cards and 9 non-face cards, of which he has a seven and a five and the dealer has an ACE showing.

What are the odds that Simon will bust if he takes one card?

Answer: The odds of Simon busting with one card is 24.4% as worked out by just two readers. Extra well done to: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Paul Knutson, textile engineer, Timken Belts, Springfield, Missouri, USA.

As Andrew Knox explained:

The odds that Simon will bust taking one card is 11/45.

This is assuming Simon considers the 10’s as one of the face cards, i.e. 10, J, Q & K are the face cards (the so-called ‘X cards’ as they all have a value of 10) and he considers the Ace thru 9 as the non face cards.

The shoe starts off with 2 decks, i. e. 104 cards, of which 72 non- and 32 face cards.

The first 4 hands deal 38 non- and 21 face cards, leaving 34 non- and 11 face cards in the shoe.

Simon has a 5 and a 7, totalling 12, so he busts (> 21) only if dealt a 10, J, Q or K, i.e. one of the face (X) cards.

The odds of this happening with 45 cards (of which 11 face cards) in the shoe is 11/45.

The fact that the dealer’s first card is an Ace is not relevant.

ps If the face cards are taken strictly as J, Q or K, then Simon cannot work out his chances exactly, as he hasn’t been counting the 10’s.