There are 100 lockers, and 100 students, each student is assigned a locker #1-100. All of the lockers start out closed, and each student goes through and changes the state (opens or closes) of each locker that is a multiple of his locker number. (i.e. locker #1 student will open every locker, while locker #2 student will close every even number locker, because even numbers are a multiple of 2)
At the end, which lockers will be open, and why?
2006-06-27 06:17:00 · 9 answers · asked by booyain 2 in Entertainment & Music ➔ Jokes & Riddles
Squared numbers have odd number of multiples. So they are opened. Total 10 are opened.
2006-06-27 06:36:55 · answer #1 · answered by ♪♫♥Šǒńǘ♥♫♪ 2 · 5⤊ 2⤋
Numbers that can be squared perfectly and 1.
1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.
All others would be hit an even amount, therefore closing the lockers. These above are hit an odd amount of times, keeping them open.
2006-06-27 14:15:29 · answer #2 · answered by Springer 3 · 0⤊ 0⤋
1,4,9,16,25,36,49,64,81, and 100.
Why: A locker will only be open if it has its state changed an odd number of times. For each time a student has a number which is a factor of the locker number, it will have its state changed once, ergo only lockers that have an odd number of factors will be open. Note: odd number of all factors, not just prime factors. However, if a factor F divides N, so does N/F, which means that all factors come in pairs, ergo the only way a number can have an odd number of factors is if one of its factors is paired with itself - that is F=N/F, which is only true for perfect squares. thus, only those lockers that are perfect squares will remain open.
Note for previous respondents: No prime numbered locker can possibly be open, since student #1 will open them and student #N will close them again and they won't be touched by any other student.
2006-06-27 13:53:33 · answer #3 · answered by Pascal 7 · 0⤊ 0⤋
lockers with prime numbers. 1, 3, 5, 7, 11 and so on..
why? because prime numbers can only be divided by itself and the number 1. so they wont be a numbered locker to close it.
2006-06-27 13:27:50 · answer #4 · answered by j o s 4 · 0⤊ 0⤋
the lockers that will be open are 1-3-5-7-9-11-13-15-17-19-21-23--25-27-29-31-33-35-37-39-41-43-45-47-51-53-55-57-59-61-63-65-67-69-71-73-75-77--79-81-83-85-87-89-91-93-95-97-99 they will be open because they r odd
2006-06-27 13:24:54 · answer #5 · answered by *******lover 2 · 0⤊ 0⤋
the lockers will end up being the same way that they started out
2006-06-27 13:30:38 · answer #6 · answered by Anonymous · 0⤊ 0⤋
Only the lockers with midgets in them will be open.
2006-06-27 13:21:59 · answer #7 · answered by sue-sue 7 · 0⤊ 0⤋
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
I actually went and figured it out. There's probably an easier way...and I probably did something wrong...
2006-06-27 14:45:37 · answer #8 · answered by čŖåŻęĤ! 4 · 0⤊ 0⤋
The 99th locker.Is that a reasonable answer?â¥
2006-06-27 13:24:57 · answer #9 · answered by Anonymous · 0⤊ 0⤋