Mr. Wolf’s 4th grade class of 20 students play a game in a hallway lined with 20 lined up lockers. the 1st student starts with the first locker and goes down the halls and opens all the lockers. the 2nd student starts with the second locker and goes down the hall and closes all the other lockers. the third student starts with the third locker and changes every three lockers: if the locker is open the student closes it, and if it is closed the student opens it. the fourth student starts with the fourth locker and changes every four lockers: if the locker is open the student closes it, if it is closed the student opens it. This process continues until all 20 students in the class have walked down the hall. a.) Which lockers are still open at the end of the game?. b.) Which lockers were touched by the only two students?. c.) Which lockers were touched by only three students? d.) Which lockers were affected the most? I haven’t found an algebraic solution. Maybe you can work on this after taking a look at the table below, where row #n is the state of the lockers (0=closed, 1=open) after the nth student passes. The last line is the number of times each locker has been hit.
01: 1111111111111111111
02: 10101010101010101010
03: 10001110001110001110
04: 10011111001010011111
05: 10010111011010111110
06: 10010011011110111010
07: 10010001011111111010
08: 10010000011111101010
09: 10010000111111101110
10: 10010000101111101111
11: 10010000100111101111
12: 10010000100011101111
13: 10010000100001101111
14: 10010000100000101111
15: 10010000100000001111
16: 10010000100000011111
17: 10010000100000010111
18: 10010000100000010011
19: 10010000100000010001
20: 10010000100000010000
1 2 2 3 2 4 2 4 3 4 2 6 2 4 4 5 2 6 2 6 thank you Steve And happy new year and God bless you