What particular feature do the following fractions have in common?
19/95, 26/65, 16/64
Answer: As Jose Padron neatly explained this is a mathematical curiosity, when cancelling the same digit in both denominator and numerator gives the equivalent of the original fraction: 19/95 = 1/5; 26/65 = 2/5; and 16/64 = ¼.
Well done and thanks for your patience, to John Bowen, consultant, Bromsgrove, UK; Jose Padron, material development specialist, Waterville TG Inc., Québec, Canada; John Droogan, advanced polymers and composites, MegaChem (UK) Ltd, Caldicot, Monmouthshire, UK; Hans-Bernd Lüchtefeld, market research & communication manager, PHP Fibers GmbH, Obernburg, Germany; and, Yuichi (Joe) Sano, Sumitomo Electric Industries Ltd, Itami, Japan; as well as to Michele Girardi, Scame Mastaf Spa, Suisio, Italy; and Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands, who were on the right track.
Also: Chair challenge
For a live webinar discussion, chairman Dave and his 11 fellow industry experts sit at a round-table. How many ways can the group be arranged, if nobody can sit between two older experts?
With apologies all round, let’s call this teaser null and void: too much confusion and difference in interpretation of the wording. A special thanks to John Droogan here for his help in sorting through this muddle.
For what it’s worth, so, below is the answer to the question, which was sourced from another journal. I should have been wary: they only received one correct answer, and that was from the editor’s brother!
There are 1024 ways, up to rotation around the table. To see this, notice that the youngest journalist must sit right next to Dave – there are two possible places for him. Then, the second youngest journalist must sit right next to this group of two. Once again, there are two possible places for him. Continuing like this, we see that for all journalist except for the oldest one, there are two possible spots on the table. Multiplying two to the power of ten out, we get 1024.