ERJ Brainteaser: August

Question 3: Off the scales

4,409, 6,614, 11,023, 15,432, ____?  (Figures rounded up)

Clues: Prime, tonnes, lbs conversion...

Answer: This time it’s hats off to Andrew Knox, Rubbond International, The Netherlands, who weighed in with the correct answer, 24,251, before any clues were issued for this tough teaser – even though he might have had a very slight advantage (see Solutions below).

Very well done also to John Bowen, rubber industry consultant, Bromsgrove, Worcs, UK; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; Michele Girardi, quality manager, Scame Mastaf Spa, Suisio, Italy; Jose Padron, laboratory analyst, Toyoda Gosei, Waterville, QC, Canada; and everyone else who had a go.

Before our clues were issued, there was also an interpretation that gave 19,841 as a valid answer. So well done also to Katharina Gottfried, technical manager, Arlanxeo Deutschland GmbH, Köln, Germany and again to John Bowen, who both provided this solution.

Solutions

Andrew Knox

These are the series of prime numbers in ascending order, i.e. 2, 3, 5, 7, in which the following is 11, converted from being metric tonnes into pounds (lb). (Rather easy for someone importing synthetic rubber from the USA in 1000 kg boxes!)

Stephan Paischer

This is a series of prime number (2, 3, 5, 7) where metric tons are expressed in pounds. The next element is 11 tonnes expressed in pounds.

Michele Girardi

If you consider these numbers as weights in pounds and you convert them in metric tons by multiplying by 0.0004535923, you get the sequence 2,3,5,7, which are consecutive prime numbers. The next in row is 11 tons, that corresponds to 24250.8 pounds.

John Bowen

Next is 24250 = these are the number of pounds [lb] in prime numbers of tonnes 2,3,5,7,11…

Katharina Gottfried

If the series is done by increasing multiply factor 4,409*1,5 - *2,5 - *3,5  - *4,5; then the next number will be 19,841.  The series would correspond to translator kg-lb pound 2kg, 3kg, 5kg, 7kg, 9kg.

John Bowen

Next one is 19841.4 This is 4409.2 x 4.5 - the previous numbers are 4409.2 multiplied by 1.5,  2.5,  3.5 so the next one is multiplied by 4.5 giving 19841.4.

Jose Padron

The next number in the series is 24251. Taking the list of prime numbers, setting this numbers as tonnes, then expressing the figures in kilograms and, finally converting to pounds.

Here is a table to show this proceeding.

Question 2: What's next?

Answer: As so nicely explained by Andrew Knox (see below) this is the series of diaphragm apertures of cameras, so the next one is 22. Well done to: Andrew Knox, Rubbond International, The Netherlands; John Bowen, rubber industry consultant, Bromsgrove, Worcs, UK; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; Michele Girardi, quality manager, Scame Mastaf Spa, Suisio, Italy; and everyone else who had a go.

Andrew Knox: These are the so-called f-stop numbers, refering to the aperture sizes of camera lenses. For a 35 mm camera the smallest sizes are usually f/2 or f/2.8, the largest f/32, f/45 or even f/64. At the other end of the scale are f/1.8, f/1.4 and f/1.2.

This is the so-called "full" scale. There are however 1/2 and 1/3 scales in between. This is an inverse scale, whereby the smaller the number, the larger the aperture. 

Aperture size affects the depth of field and the required exposure time for conventional light-sensitive film. Each step in the full scale f-stop numbers either halves or doubles the exposure time required.

Question 1: High five!

Can you find the link between: Automobile, Buenos Aires, Mozambique, Sequoia (tree) and Tambourine?

Answer: You either saw it or you didn’t: all five words contain all five vowels in the English language – A, E, I, O, U.

Very well done to: Dr Veronika Beer, sustainable development, wdk Wirtschaftsverband der deutschen Kautschukindustrie eV, (German Rubber Manufacturers Association), Frankfurt am Main, Germany; John Bowen, rubber industry consultant, Bromsgrove, Worcs, UK; Jose Padron, laboratory analyst, Toyoda Gosei, Waterville, QC, Canada; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; Andrew Knox, Rubbond International, The Netherlands; Michele Girardi, quality manager, Scame Mastaf Spa, Suisio, Italy; and everyone else who had a go.