ERJ Brainteaser: April

Please complete the following:

Norway, Sweden, Burma, Austria, Peru, Egypt, Ghana, South Korea, ___.

Clues during the week if readers are struggling...

Email your answer: correct replies on Friday.

What should come next in the following series?:

Boron, Nitrogen, Sodium, Aluminium, Chlorine, …

Answer: Not our toughest ever teaser, but not our easiest either. The atomic numbers of these elements give a series of prime numbers, making the next element potassium, which has an atomic number 19. 
Well done to: Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; Francesco Parazzoli, R&D - material development, new raw materials, Pirelli Tyre SpA, Milano, Italy; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Michael Easton, director, Globus Group, Trafford Park, Manchester, UK; John Bowen, rubber industry consultant, Bromsgrove, Worcs, UK; Stefano Carletti, R&D, Indorama Mobility Group. Office address Glanzstoff Sicrem Spa, Pizzighettone (CR), Italy; Michele Girardi, Scame  Mastaf Spa, Suisio, Italy; France Veillette: chef environnement, Usine de Joliette, Bridgestone Canada Inc., Canada; Daniel Willrich, redakteur, büro Köln, AutoRäderReifen-Gummibereifung, Köln, Germany; Jose Padron, material development specialist (many thanks for the illustration), Waterville, Québec, Canada; and everyone else who had a go. We might also flag up Italy as the top country this week, with three correct replies.

New teaser on Monday

Maths expert Matt is studying his 24-hour digital clock, which displays the time in hours and minutes. He decides to work out what proportion of the day does it display at least one '1'. What should Matt’s answer be?

Answer: Readers were left all in a daze by this one except for three top Brainiacs, who worked out the answer as 62.5 %. Extremely well done in order of reply to: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Michele Girardi, Scame  Mastaf Spa, Suisio, Italy; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; and everyone else who had a go. 

Solutions

Andrew Knox
In the 12 hours that do not have a "1" in them, (i.e. 00, 02, 03, 04, 05, 06, 07, 08, 09, 20, 22, 23) there are 15 minutes which do contain a "1", i.e. 01, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, so 12 x 15 = 180 minutes.
In the other 12 hours that do contain a 1, every minute of the hour will contain at least one "1", so 12x60 = 720 minutes.
So, proportion of minutes in 24 hours that contain at least one "1" is (180 + 720)/(24 x 60) = 900/1440 = 62.5%

Michele Girardi
There are 60 numbers for minutes, 15 have one's, 45 not
- there are 24 numbers for hours , 12 have ones, 12 have not
- there are 24*60 = 1440 possible displays in one day
- of these 45*12 = 540 have no ones
- the percentage of displays with at least a one is ( 1440-540)/1440= 62,5%

Stephan Paischer
First digit:         1x:xx                10 hrs (from 10:00 – 19:59)
Second digit:    x1:xx                2 hrs (overall it happens 3 times per day, for 1 hr each, but one hour is already covered by the first digit)
Third digit:        xx:1x                2 hrs (overall it happens 10 mins per hour, but to be considered only for the remaining 12 hrs – so 12 x 10 min = 120 mins)
Fourth digit:      xx:x1                1 hr (overall it happens 1 min every 10 mins, but here to be considered only 5 times for every of the remaining 12 hrs, as 1 from the 6 times is already covered by the third digit, so 5 x 12 = 60 min)
Total 15 hrs, this is 62,5% of 24 hrs.

New teaser on Tuesday