ERJ Brainteaser: August

What comes next in the following series:

S, M, H, D, W, M, ?.

Answer: If you didn’t get this teaser straight away, you either didn’t get it at all, or went on a very wild goose-chase. No such travails, though, for five of our finest Brainiacs, who worked out that the letters indicate the units-of-measurement for time: Second, Minute, Hour, Day, Week and Month, making Y for year the answer Well done to: John Bowen, rubber industry consultant, Bromsgrove, UK; Jose Padron, material development specialist, Waterville TG Inc., Waterville, Québec, Canada; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; David Mann, key account manager, SPC Rubber Compounding, UK; Michele Girardi, Scame  Mastaf Spa, Suisio, Italy; and everyone else who had a go.

New teaser on Tuesday.

In a best-of-three-sets tennis tournament with 64 players, what is the minimum number of shots a player would have to hit to emerge as champion?

Answer: Taking into account that every opponent could – like me sometimes – double fault throughout the entire match, then the answer works out at 144 shots as neatly explained by Andrew Knox Rubbond International, Ohé en Laak, The Netherlands; and John Bowen, rubber industry consultant, Bromsgrove, UK.

But, as this was a bit of a trick question, our judging panel also accepted 288 shots. So well done to: Natalie Prescott, product manager, dynamic testing, Prescott Instruments Ltd, Tewkesbury, Glos., UK; Michael Easton, sales and marketing director, Globus Group, Manchester, UK.

Serving up the most stylish solutions were:

Andrew Knox

When playing a non-service game, the server will need only 4 shots to lose each game, if all his shots are out. As receiver, his opponent doesn't need to play a shot at all to win the game.
So the answer in fact is a minimum of 4 shots to win each of 3 service games with aces (=12 shots), and no shots at all to win the 3 non-service games, which is 12 shots to win a set, or 24 shots to win 2 sets and the match. 
As there are 6 matches in total to play, including the final, then a minimum of only 6 x 24 or 144 shots would be required to win the tournament

Natalie Prescott

Game, set, match:
4 points to win a game
6 games to win a set
2 sets to win a match
Min. number of shots to win = 4*6*2 = 48
64 player tournament:
R64, R32, R16, quarter-finals, semi-finals, final – 6 matches to win
Alternatively, log2(64) = 6
Min. number of shots to be champion = 48*6 = 288

It takes Donald 60 minutes to wash a car. How long would it take if he is joined by Joe working 10% faster? 

Answer: As the solutions below show, there were several interesting routes to the correct answer, 28.57 minutes. So very well done this time, in order of correct reply, to: John Bowen, consultant, Bromsgrove, UK; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Jose Padron, material development specialist, Waterville TG Inc., Waterville, Québec, Canada. Also on the right track, though with a different interpretation, were: Lionel Lesage, CU Valves Dept, KSB Gradignan, Gradignan, France; Dr. Jens Kiesewetter, director applied technology tire & R=rubber: silica & silanes, Evonik Operations GmbH, Smart Materials, Wesseling, Germany. Well done to all above and everyone else who had a go.

John Bowen
Time working together is 28mins 34 secs
[Don's work rate is 1/60 car per munute, ie 0.0166667/min
Joe's work rate is 10% faster, 0.0183333/min
Together, the rate is the sum of these, 0.035/min, so to do 1 car requires 1/0.035 = 28.57 minutes, or 28min 34 sec

Jose Padron:
Donald and his dude would take 28.57 (29 min. rounding up) minutes to wash a car.
Here is how:
Donald Speed = 1 car / 60 min = 1 car/hr. = t
Dude speed = 1.1 car / 60 m in = 1.1 car/hr.
Donald + dude = 2.1 / 60 min = 2.1 car/hr. = t’
From classical equation speed = Number of cars / time; s = #car / t
As they wash only one car, this become #car = s * t:
Thus, making an equation for both conditions:
(Donald’s) s * t = (Donald+ dude) s’ * t’
Solving for t’ = (s * t)/ s’ = (1 * 60)/2.1 = 28.57 minutes.

Andrew Knox
If Joe is working 10% faster than Donald, then his output is 11 cars in the time it takes Donald to wash 10.
So Joe takes 60/1.1 = 54.54545454545 minutes to wash a car.
(You might argue 60 minutes minus 10% is 60 - 6 = 54 minutes, but this is not correct, as in 600 minutes, Joe would be able to wash 11.1111.. cars).
So Donald washes 1/60 cars/minute and Joe 1/54.5454545454.. cars/minute. After X minutes working together, X/60 + X/54.5454545454... must = 1.
So X is therefore 1/(1/60 + 1/54.5454545454...) = 1/0.035 = 28.57 minutes.

Which city completes the following series?

Sarajevo, Bern, Sofia, Madrid, _.

Answer: Continuing a strong run of form, our high-flyer this week was Andrew Knox, who came up with the correct answer first thing on Monday, ie without any clues. Andorra la Vella completed this series of European capital cities based on their height above sea-level

Well done, so, to: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; John Bowen, consultant, Bromsgrove, UK; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; Jose Padron, material development specialist, Waterville TG Inc., Waterville, Québec, Canada, and everyone else  who had a go.

Extra thanks to Jose Padron for this neat table: