6 boys pick a captain by forming a circle then eliminating every n'th boy. The 2nd boy in the counting order can choose n. If he wants to be captain what's the smallest n he should pick?

• The 2nd boy in the counting order can choose n. If he wants to be captain ,
  the smallest n he should pick should be 10.
• 12 years agoHelpfull: Yes(2) No(1)
• Let the boys names be A B C D E F and let counting start from A.
  Since B decides n,we have to check the elimination sequence for each n and find in which B stays in the end.
  for n=1,ABCDEF-BCDEF-CDEF
  for n=2,ABCDEF-ACDEF
  for n=3,ABCDEF-ABDEF-ABDE-ABE-AE
  for n=4,ABCDEF-ABCEF-ACEF
  for n=5,ABCDEF-ABCDF-ABCF-ABC-AC
  for n=6,ABCDEF-ABCDE-BCDE-BDE-DE
  for n=7,ABCDEF-BCDEF-BDEF-BDE-DE
  for n=8,ABCDEF-ACDEF
  for n=9,ABCDEF-ABDEF-BDEF-DEF
  for n=10,ABCDEF-ABCEF-ABEF-ABE-BE-B
  thus minimum n is 10
  
• 12 years agoHelpfull: Yes(1) No(1)
• .................................
• 12 years agoHelpfull: Yes(0) No(2)