The Locker Proble

1 4 9 16
1o 1o 1o 1o
2c 3c 2c
4o 9o 4o
8c
16o

In my group we figured out that the lockers that are going to be opened are the perfect squared numbers. The reason that is because every perfect squared has an odd amount of factors (See the example on the bottom if you don’t understand why they have an odd amount of factors). It's like a pattern opened, closed, opened, closed, etc. If there is a even amount of factors then its going to land on a closed, and if theirs a odd amount of factors it's going to land on a open. Like the example above those are perfect squared numbers, and the o and c stand for open and closed. As you could see all of them land on open. For example after 16 it's not going to be touch anymore because the 17th student would skip it, so that means it wouldn't be touched anymore, and then 18 would skip it to, and so on. At the end of this all we came out to 31 lockers being open because that it the last perfect squared number that doesn't equal more then 1,000. And if we if it was 32 squared then the sum would end up being more then 1,000

The number 16 has an odd amount of factors and 15 have an even amount. The factors for 16 are 1, 2, 4,8,16 and the factors for 15 are 1, 3,5,15. As you could see for 15 the factors each have a pair, 1x15 & 3x5. But if you look at 16s factors they don’t each have a pair. It’s 1x16, 2x8, but what about the 4. The four doesn’t have a pair. That is the reason why perfect squares have an odd amount of factors