ERJ Brainteaser - March

As a leaving present from his colleagues at work, Simon is given an electric analogue wall clock. On the 1st of May, he sets it up at home moving the hands to the correct time, 8.30h in the morning. However, as it was bought on a very small budget, the timepiece is not that accurate: gaining ten minutes every 24 hours. But while he viewed it at 8.30 every morning, Simon never reset the clock to the correct time. At 8.30 one morning it showed the time as 2.30h. What was the earliest date on which the clock could have shown this time? 

Answer: Quite straightforward this week, though the question did garner different interpretations (see below). But the correct answer was 6 June, as provided in order of reply by: John Bowen, consultant, Bromsgrove, UK: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Paul Knutson, textile engineer, Timken Belts, Springfield, Missouri, USA; David Mann, key account manager, SPC Rubber Compounding, UK; France Veillette, chef environnement, Usine de Joliette, Bridgestone Canada Inc., Canada: Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria. Yanwen Zhou, Conti, China. Congratulations to all above and everyone else who had a go.

As John Bowen neatly explained: 
2.30 is 6 hours ahead, so with a gain of 10 minutes or 1/6th hour/day this will be 36 days on, which will be 6th June.

A different interpretation by Jose Padron and Michele Girardi put the clock 18 hours ahead, making the answer 17th August. 
 

In a healthfood factory lab, Simon is perfecting the ingredients for a new breakfast cereal. Using a two-pan weighing balance, he finds that a pan containing 7 spinach flakes is precisely balanced when two carrot flakes and one apple flake are placed in the opposite pan.

Also, he finds that a pan containing 6 carrot flakes is exactly balanced by five spinach flakes and one apple flake in the opposite pan. Next he places five spinach flakes and four carrot flakes into one of the pans.How many apple flakes does Simon need to put into the opposite pan to balance the scales?

Answer: If Simon hadn’t dropped a flake somewhere, the answer would likely have been a whole number. Undeterred, some of our top Brainics weighed in with the correct answer 2.75. Extra well done in order of reply to: Paul Knutson, textile engineer, Timken Belts, Springfield, Missouri, USA; 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: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Jose Padron, material development specialist, Waterville TG Inc., Waterville, Québec, Canada.

John Bowen showed how this tasty teaser could be neatly resolved:

Let Spinach = S, Carrot = C, Apple = A

1] 7S = 2C + A

2] 6C = 5S + A

By rearranging and subtracting simultaneous equations, S = 1/4A and C = 3/8A

To find the number of apple flakes, = 5S + 4C = 1 1/4A + 1 1/2A = 2 3/4
 

At a baked beans factory, the packaging line is supplied with cans manufactured from three pieces: one long strip measuring 235mm X 110mm to form the body of the can; and two circular end pieces each of diameter 75mm, which includes the rim of the can.

How many cans can be made using a sheet of metal measuring 675mm by 770mm?

Answer: Not so many takers for the deceptively difficult teaser. But showing a can-do attitude to come up with the correct answer, 14, were in order of reply: 

Hans-Bernd Lüchtefeld, marketing manager – automotive safety, Indorama Mobility Group, PHP Fibers GmbH, Obernburg, Germany; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Michele Girardi, Scame  Mastaf Spa, Suisio, Italy; Lionel Lesage, CU Valves Department T-VA V222, KSB, Gradignan, France; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; Paul Knutson, textile engineer, Timken Belts, Springfield, Missouri, USA; David Mann, key account manager, SPC Rubber Compounding, UK; Jose Padron, material development specialist, Waterville TG Inc., Waterville, Québec, Canada.

Not for the first time, readers came up with some really stylish answers:

Jose Padron
The area of the sheer of metal = 675 * 770 = 519,750 mm²
The area of one can is Area rectangle + area of two circles = (235 * 110) + (3.1416 * (75/2)² = 25850 + 8835.75 = 34685.75 mm²
Number of cans = Area of the sheet of metal / Area of one can = 519750/34685.75 = 14.9 cans
So the number of cans must be an natural digit, so they are: 14 cans
However, how the metallic sheet should be cut to have these 14 cans is the tricky part. Here is the proposition for working the maximum of the sheet of metal:

David Mann
Dividing the sheet by the strips and lids needed to make a can, theoretically you could make 14(.98). So how to do it?
As the long side of the sheet is a multiple of the short side of the strip, a 2 x 7 arrangement works here. That leaves an area of 77 x 20.5cm to make 28 lids.
Luckily, if the centres of the circles are arranged in a hexagonal pattern, three rows can be fitted in as the distance required is only 20.49cm.
There's also enough length to fit 9 circles in 2 rows and 10 in the centre.

Lionel Lasage:

Simply:

What number comes next in this series?
318, 342, 366, 474, 586, _,

Answer: This one knocked many readers – including some of our most experienced Brainiacs – for six (cricket term). But not, in order of sending in the correct answer 826:

Michael Easton, director, Globus Group, Trafford Park, Manchester, UK; France Veillette, chef environnement, Usine de Joliette, Bridgestone Canada Inc., Canada; Michele Girardi, Scame  Mastaf Spa, Suisio, Italy; Lionel Lesage, CU Valves Department T-VA V222, KSB, Gradignan, France. Congratulations to all and everyone else who had a go.

Come on other Brainiacs, it wasn’t that difficult, as neatly shown, for example, by:

France Veillette
The next number of the series is given by adding the multiplication of the digits: 826 = 586 + (5x8x6)

and

Michele Girardi
318
342 = 318+24 = 318+3*1*8
366 = 342+24 = 342+3*4*2
474 = 366+108 = 366+3*6*6
586 = 474+112 = 474+4*7*4
826 =                   586+5*8*6