There is a school with 100 students and correspondingly 100 lockers, all of which start off closed. The first student opens every locker and the second students closes every other locker starting with the second (2,4,6...etc..) . The 3rd student changes the state of the lockers numbered (3,6,9.. etc.). The fourth student changes the state of the lockers numbered (4,8,12.. etc..).. This continues until all the 100 students passes along the lockers.. when all the 100 student is done which locker is closed and which locker is in open condition?

• the lockers 1^2,2^2,3^2,.....,10^2 will be opened(i.e) 1,4,9,.....,100 will be opened others will be closed
  hence 10 lockers will be opened
• 9 years agoHelpfull: Yes(24) No(1)
• The perfect square one's
• 9 years agoHelpfull: Yes(12) No(0)
• Only perfect square Number's are opened...
  
  Example: Take Only 10 doors.
  only 1 , 4, and 9 number door's are opened....
  Simillary 1 to 100 All perfect squrare no. are open
• 9 years agoHelpfull: Yes(10) No(1)
• wahen calculating for first 10 doors we come to know a pattern that the squared numbered doors are open.Henceforth we come to a conclusion that squared numbers from 1-100 i.e 1,4,9,16,25,36,49,64,81,100 will be open and the rest doors will be closed.
• 8 years agoHelpfull: Yes(5) No(0)
• 1 -> 1,2..100 (open) [ consider only unit digits]
  2 -> 2,4,6,8,0 (close)
  3-> 3c, 6o,9c,2o,5c,8o,1c,4o,7c,0o
  like thqt upto 10
  when
  9 -> 9c,8c,7c,6c,5o,4c,3c,2c,0o
  10-> 0c
  after 100 students passes
  the doors with unit digits 5 will be in open condition
  all other doors are in closed conditon
• 9 years agoHelpfull: Yes(4) No(15)
• locker one will be opened atlast
• 9 years agoHelpfull: Yes(3) No(3)
• lockers that are opened- 1, 4, 9, 16,25, 36, 49, 64, 81, 100
  lockers that are closed- 2,3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99
• 6 years agoHelpfull: Yes(2) No(0)
• Answer:256
• 8 years agoHelpfull: Yes(1) No(4)
• 1 is the answer because all lockers will be closed by 2,3,4,5........100 except first one
• 8 years agoHelpfull: Yes(1) No(6)
• lockers that are closed- 1, 4, 9, 16,25, 36, 49, 64, 81, 100
  lockers that are opened- 2,3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99
• 8 years agoHelpfull: Yes(0) No(9)
• 11
  2 --> 2,4,6,8,10,12
  3--> 3,6,9,12,15
  4--> 4,8,12,16,20
• 8 years agoHelpfull: Yes(0) No(0)
• the square one's will be opened , the square no's 1 to 100 , there are totally 10 square no's, so 10 doors were opened
• 8 years agoHelpfull: Yes(0) No(0)
• 10 doors will be oped.
  door no 1,4,9,16,25,36,49,64,81,100 will in open others will b closed.
• 8 years agoHelpfull: Yes(0) No(0)
• all the perfect squares numbers from 1 to 100 get opened all other are closed because perfect squares has odd multiples eg 4 has 1,2,4
• 8 years agoHelpfull: Yes(0) No(0)
• Each 5th student opens all the locker since the pattern of these 4 students completed and hence the 100th student will be opening all the lockers and hence no locker is left in closed condition
• 7 years agoHelpfull: Yes(0) No(0)
• Odd lockers are open even lockers are closed
• 6 years agoHelpfull: Yes(0) No(0)
• 9.that is the number of perfect squares below 100
• 6 years agoHelpfull: Yes(0) No(0)