I'm in some desperate need for help on this problem I can't seem to fully wrap my head around...(the answer is perfect squares due to odd # of factors, but I must explain it clearly!! How?)
There are 1000 open lockers at a school, one locker for each of 1000 students. The first student comes in and closes all the lockers. The second student comes ina nd changes the condition of each second locker (so if a locker is closed, it is opened, and if a locker is open, it is closed). In other words, the second student opens lockers #2, 4, 6, 8, ...., 1000. Then the third student comes in and changes the condition of each third locker, i.e. opens locker #3, closes locker #6, opens locker #9, etc. The fourth student changes the condition of each fourth locker, the fifth student does so for each fifth locker, and so on, until eventually the 1000th student comes in and changes the condition of the 1000th locker. Which lockers are now closed??
2007-11-13
16:28:18
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3 answers
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asked by
netsurfer733
2
in
Mathematics