Can you start off this series, written to three decimal places?
__, 0.750, 0.833*, 0.875, 0.900, 0.916*.
*Last digit is recurring
.For his admirable hand-written and drawn answer to (hotly contested) Q1, the top award goes to Rohit Kale of Michelin, our new Brainiac of the Month.
Answer: This is a series of fractions 1/2, 3 / 4 , 5 / 6, 7 / 8, 9 / 10 and 11 / 12 written in decimal - making the answer 0.500. On the mark this week were: John Bowen, rubber industry consultant, Bromsgrove, Worcs, UK; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Rohit Kalé, distribution strategy manager, AMN/V/B2C/DIS, Michelin North America Inc., USA: Michele Girardi, Scame Mastaf Spa, Suisio, Italy. Well done to all five, and everyone else who had a go.
When the inverse of these numbers is calculated, they become 1.33,1.2, 1.14,1.11, 1.09 [recurring] which may be written as fractions 1 1/3, 1 1/5, 1 1/7, 1 1/9, so the inverse of the first one would be 1 1/1 or2, so the first one would be 0.500.
Expressed as fraction, the series goes as follows:
¾, 5/6, 7/8, 9/10, 11/12.
Both numerator and denominator are increasing by 2 for every step, so for the initial step we decrease both by two (from ¾): that gives ½, so 0,500.
Every number of the series is an odd number divided by the following even number
1/2 = 0,50000
3/4 = 0,75000
5/6 = 0,83333
7/8 = 0,87500
9/10 = 0,90000
11/12 = 0,91667
When you convert all the decimals into fractions, you would see the pattern in the fractions where for each next decimals both the Numerator and the denominator increases by 2.
Hence from 0.750 which converts into ¾, if you subtract 2 from both from Numerator and denominator it comes out to be ½, which is 0.500 as a start of the series.
New teaser on Monday