0

Select three people out of 10 sitting in a circle such that no two of them are consecutive?

In the above post, @true blue anil has given answer, where he has written "but each unit is getting only 7 starting points instead of 10". I am not understanding that part. And Anil has not been active here since March. So, I decided to ask my doubt in a separate post. I hope it's not against the rules here. Are there any links to understanding that part? Thanks.

aarbee
  • 8,246
  • Anil reimagined the scenario as involving some "big" objects which occupy two seats at once and "small" objects which occupy only one seat at once. If we were to imagine letting the "big" objects each just sit in one "big" chair rather than simultaneously taking up two "small" chairs... then to let them all sit around the table we only have need of seven chairs overall. – JMoravitz Sep 03 '20 at 17:24
  • @JMoravitz I can understand how we got 35. But I am not understanding how we got 50. – aarbee Sep 03 '20 at 17:28
  • The interpretation used in the linked question is that we care about where true-north is. In the chair metaphor, one of the seven chars could be sitting in the north position. Now... reimagining back to small chairs in place of big ones, think of it as though the only possibilities we counted were for the left chair of a pair of chairs who were formerly big could have been in the north position. We are missing out on what happens if it were the right chair of a pair of chairs who should have been the north position. – JMoravitz Sep 03 '20 at 17:36
  • 1
    We might have been able to correct the count earlier by being more careful, but in Anil's answer they opted to just correct the count at the end by multiplying by $\dfrac{10}{7}$, effectively forgetting where north was for the larger chair scenario by dividing by $7$ and then picking where north was for the only small chair scenario by multiplying by $10$, now making it so that all ten of the small chairs were possible positions of true north rather than having missed the scenarios where the rightmost of the paired chairs was north. – JMoravitz Sep 03 '20 at 17:38
  • @JMoravitz Thanks. Care to convert this as an answer so that I could accept it? – aarbee Sep 03 '20 at 17:39

0 Answers0