A book contains 30 stories. Each story has a different number of pages under 31. The first story starts on page 1 and each story starts on a new page. What is the largest possible number of stories that can begin on odd page numbers?

• The question is to maximise the number of stories starting with odd numbers, so if a story has to start with an odd number, the number of pages(total) upto the previous story must be even.
  
  So, we have to make sure the total must be even for maximum number of times.
  
  So, we should not put one odd number and one even number, as the total becomes odd in this case.
  So, if i put two odd numbers as a group, the total will be even
  Another pecaution that we should take is not putting three odd numbers, so after every two odd numbers we should put even numbers..
  
  But inspite of all these precautions, we cannot avoid some cases where the sum will be odd, because of the odd numbers.
  Of the fifteen odd numbers we can avoid the case for 7 of them, but for eight
• 11 years agoHelpfull: Yes(1) No(0)
• For the remaining seven numbers we cannot avoid. So, maximum possible is 23.
  
  Answer is 23.
  
  I am giving an example arrangement to better understand.
  
  2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,1
  Above numbers are the number of pages in each of the first 16 chapters, all of them are starting with odd numbers, as the sum of all the numbers is even in each case
  
  Now after 1, the next chapeter should with even page, because the sum become odd
  This cannot be avoided
  
  So, next will be
  3,5(starts with odd page), 7, 9(odd ) 11, 13(odd) ,15,17(odd) ,19,21(odd) ,23,25(odd) 27,29(odd page)
  
  So, total is 16+7 = 23 stories start on odd numbered pages.
  
  Answer is 23
• 11 years agoHelpfull: Yes(1) No(0)