Top And Bottom Lockers? The 13 New Answer

Credit: Brett Levin/flickr (CC BY 2.0)

It’s less complicated than you might think.

A school has exactly a thousand lockers, numbered 1-1000, and a thousand students. Every year, on the last day of school, the Headmistress holds a graduation ceremony, during which she enlists the help of her students to close the school’s lockers.

She assigns each student a number and asks him or her to help her one at a time. These are the instructions she gives to each of the students.

Student #1: Go to each locker and open it.

Student #2: Go to every other locker and close it.

Student #3: Go to every third locker. If it’s closed, open it, and if it’s open, close it.

Student #4: Go to every fourth locker. If it’s closed, open it, and if it’s open, close it.

This continues until Student #1000 is finished.

After the graduation ceremony is over, the Headmaster walks through the school and locks any lockers left unlocked. How many lockers does the client close?

A notice:

Test it out with just ten lockers and ten students and see if you can find a pattern.

Solution:

The client only has to close the lockers whose numbers are perfect squares. This means the solution is as simple as finding the square root of the highest possible perfect square within 1000.

31*31 = 961

32*32 = 1024

So 31 is the number of lockers that the client has to close.

Pictured below is the solution with ten lockers and students.

X=locker closed

O=open locker

Here’s what happens to the lockers from the first to the third student…

1 2 3 4 5 6 7 8 9 10 O O O O O O O O O O O X O X O X O X O X O X X X O O O X X X

And the tenth grader…

O X X O X X X X O X

The lockers that remain open after the tenth student is done are lockers 1, 4, and 9 – the only three perfect squares among 10.

The solution may become more obvious if you look at a specific locker and add up the number of students who opened it and the number of students who closed it.

The total is equal to how many factors the number of that locker has. Every time a student opens or closes a specific locker, it implies that the number assigned to the student is a factor of that locker number.

Since the lockers are closed from the start, any time a locker number has an even number of factors, it will be closed. Numbers with an odd number of factors will end up being open. All perfect squares have an odd number of factors, which is why the lockers with those numbers end up open while others end up closed.

Was that too easy for you? Try a harder one here.

h/t: pzzls.com

Getting a new locker is a ritual part of going to school.

Will you be lucky enough to get one outside of your classroom in a corridor so you can access it at any time? Or a locker in a convenient central location where you can pop in between classes to pick up a textbook? Maybe lose out this year and get a locker that sits right on top of a radiator; Bliss when you pull out a clean PE kit in the middle of winter, warmed up nicely but uncomfortable when you had PE first and your stinky kit has been cooking in it all day…

Wherever your locker ends up, it’s a useful resource for your time at school, especially if you happen to be assigned a decent-sized locker. It’s the only place in the school that’s completely yours, under lock and key. You should leave most of the space in it free to store your sports equipment, textbooks, notebooks and other school supplies. But if there’s still room left when all those things are already tucked away in there, you might want to consider how best to use the rest of the space. Here are our top suggestions for what to keep in your locker this year that won’t take up too much valuable space. You’re prepared for anything when you have all of these things—but having even a few should leave you enviably equipped for the challenges and surprises of the school year to come.

1. A spare pair of tights or socks

Is there anything worse than walking around all day in wet socks when your shoes have worn out, or in tights with a hole your toe is sticking through and threatening to cut off circulation? Tights or socks – depending on your preference – take up very little space in your locker and on the day when it decided to pour down rain if you were wearing summer shoes to school, you’ll be very thankful to have them.

2. An umbrella, hat or foldable poncho

There are other plans you can make for unexpected weather changes. If you have enough space for a folding umbrella, your locker capacity must be enviable, but most lockers should be able to accommodate a beanie hat to keep your hair dry in a deluge, or at least the mac-in-kind kind of A sack or plastic poncho that you can buy at bus stops for a few pounds. You won’t look glamorous, but you will look dry, and by the coming school year you might be willing to make that trade.

3. A mirror

In girls’ restrooms at school, mirror space (especially when the mirrors are directly above the sink) can be highly competitive. With guys, you might find it easier to get a mirror, but you’re more likely to make fun of it for caring about your looks. But everyone has had the experience of getting spinach in their teeth and getting it out. Make it easier on yourself by keeping a small mirror in your locker – you can even hang it inside for added style.

4. A toothbrush, dental floss, or breath mints (or all three)

A small collapsible toothbrush and a tube of travel toothpaste take up very little space, and a roll of dental floss or a can of Tic Tacs take up even less space. But they could be a lifesaver if you’re going for lunchtime garlic bread. It’s also handy if you’re having an impromptu sleepover at a friend’s house and don’t want your mouth to feel fuzzy the next day.

5. Other personal hygiene items

Likewise, there are other personal hygiene items that you may wish to have on hand. That can be sanitary protection, a small roll-on or aerosol deodorant, a comb or any other personal hygiene item you find essential — maybe even dry shampoo if you haven’t had a chance to shower after PE. Buy travel miniatures to avoid all of this taking up too much space.

6. Sunscreen

If you live somewhere where the weather is unpredictable, you get sunburnt easily, or both, remember that a small tube or spray bottle of sunscreen does indeed take up very little space and you’ll make the most of an unexpectedly sunny lunchtime could without looking like a tomato for the next two weeks. You might think that the start of the school year in September is a silly time to stuff your locker with them, but the chances that you’ll remember when April’s first day of a heat wave is are extremely slim.

7. A popular paperback

An extra book sounds like it’ll take up a lot of storage space, but a cheap, slim paperback doesn’t have to take up too much of your valuable locker space. There will be times when you will be unexpectedly delayed at school, or your journey home will take longer than usual, or you are waiting for an afternoon club and have no homework to catch up on. It’s convenient to be able to pick up a book you like even when the school library is closed. Additionally, if certain points of the upcoming school year are proving stressful, spending a little time in your favorite fictional universe is a great way to make yourself feel better.

8. Enough money for a bus ride

Sometimes you leave your handbag or wallet at home, sometimes you have to pay for a school trip quickly, sometimes something gets lost or stolen and sometimes you simply fancy something special on this day in the school canteen. You can keep a bad day from turning into a worse day by making sure you always have the means to get home and saving yourself an embarrassing phone call to your parents.

9. A long-lasting snack

It’s hard to concentrate when you’re hungry. There will be days when you have to leave the house without breakfast or when all the canteen offerings inexplicably contain something you are allergic to. Find a snack that won’t go horrible unless it’s always stored in a cool, dry place, and has an expiration date well into the future, and keep one or two in your locker. And then remind yourself that it’s okay to eat them on days when you’re just really hungry, as well as during emergencies.

10. A calculator

We didn’t include most of the things your phone can do on this list (such as a flashlight, map, camera, or notepad) because you can assume you’ll be there for whatever you do outside of the school have to do, you have access to your phone. But understandably, your school might not like you using your phone in a math or science class when you left your calculator at home. So save yourself the hassle and keep reserves ready. Even a simple mini (like the kind you might get on a keychain) can be of help.

11. A mini first aid kit

It’s quite embarrassing to have to go to the school nurse or the like for every little ailment, especially when you have to fill out a case book for every silhouette. We’re not suggesting you keep a full first aid kit in your locker, complete with bandages and burn cream (please go to the school nurse if this might be required), but you can keep essentials handy – for example a some plasters, a simple pain reliever like acetaminophen or aspirin, and a packet of cough drops.

12. A birthday card

Forgetting a friend’s birthday is embarrassing, yet it happens to us all. If you log onto social media over breakfast and the first thing you see is a notification telling you it’s a friend’s birthday, help yourself out of the nightmare of forgetting something so important by keeping a card in your locker. With a bit of skill, you can use it to write a promissory note or voucher (e.g. for a surprise day), which also prevents you from forgetting a gift.

13. A deck of cards

Secondary school is full of opportunities when you are with a group of people who have something to do. Maybe it’s a rainy lunchtime when you were planning to play soccer, or your theater group is waiting for your rehearsal space to open. A deck of cards takes up very little space but could save the day. It doesn’t even have to be a traditional deck of cards if that’s not to your liking – with no packaging, a game like Coup could fit nicely in a locker instead. Just don’t be tempted to play with your friends, even if it’s just for candy – you could get into all sorts of trouble depending on your school’s code of conduct.

14. A plastic spork

If you bring your own lunch but forgot a fork for your salad or a spoon for your yogurt, save yourself the hassle of begging for one in the canteen by providing a spare plastic spoon (a hybrid of a spoon and a Keep spoon) fork) in your locker. You can carry a spare when you buy a takeout salad and just stash it when you need it.

15. A spare hair tie

If you have long hair, going without a hair tie can be an utter pain. You may need to tie your hair back so it doesn’t get in your eyes when you exercise, or so you don’t set it on fire in a chemistry experiment. Yes, you can usually get an elastic band as a replacement, but that can get tangled and ruin your hair. A spare hair tie in your locker takes up no space at all.

16. Nail clippers

You probably can’t get away from keeping a full Swiss Army knife in your locker (nor should you!), but a set of nail clippers should be in order, giving you the opportunity to trim or file your nails if necessary. If this seems unnecessarily vain, wait until you get a split nail or hangnail; At this point, you’ll be grateful to have a pair of nail clippers. You might even get them from a Christmas cracker.

17. Glasses or sunglasses

If you need glasses for vision, it’s always wise to have a spare pair of glasses with you, as they can be so easily misplaced or smashed – and it’s inevitably that day when you have a mock exam and really need to be able to see. Even if you have perfect vision, a pair of sunglasses can be a handy thing on hot days when the sunscreen that’s also in your locker comes in handy.

18. A phone charger

In the days of universal chargers, you probably have an extra phone charger at home, so bring it to school and save yourself all sorts of trouble when you forget to charge your phone or accidentally leave the flashlight on and that Device empty battery. Also, the USB charger could come in handy if you don’t have a memory stick and want to save a file from the school computer system; Instead, just put it on your phone.

19. A list of important phone numbers

A phone charger comes in handy, but if your phone is dead beyond the level that a quick charge can fix, you could be a little stuck. You probably know your home landline number by heart, but what about your parents’ and friends’ phone numbers? If your phone is beyond repair, you might want to call your parents to let them know, but you’ll have trouble if your only record of their number is on your phone itself.

20. A small bag of long-lasting candy

Because in a stressful school year you will definitely need a pick-me-up at some point, so a couple of Haribo Coke bottles or flying saucers could be just the thing.

What are your locker essentials? Let us know in the comments!

Pictures: tights; girl with umbrella; girl with mirror; Toothbrush and toothpaste; makeup brushes; woman applying sunscreen; Books; bus seats; snack bars; Calculator; first aid bag; birthday card and pen; playing card; sporks hair band; nail clippers; Glasses; telephone and cell phone batteries; list; Sweets; Lockers; locker key

More and more offices are opting for “hot desk” arrangements with no assigned seating. More and more of us are living without the paraphernalia we consider essential to our work environment, photos of our pets, notebooks, our ever-convenient highlighters, and of course, snacks.

Offices using this setup usually provide a storage solution in the form of lockers – similar to the ones we had in high school minus the random stickers of our favorite bands or other junk. If you work in such a facility, the following list of things will come in handy to make your office locker better than those teen TV shows.

locker

If you only have 1 square foot to work with, a locker shelf is mandatory to ensure you can store enough of your belongings. Make sure you measure your locker before purchasing a locker rack. A good roll of the thumb is to look for lockers that have ample space underneath to give you some space to store any books and binders you may have. You can even stack another shelf if you have enough headroom.

replacement headphones

You don’t want to take your top-of-the-line gaming headphones to the office unless you intend to misplace them or even lose them altogether. If you’re the type who doesn’t like messy cords, you can even opt for a wireless one. Here’s a list of the best headphones for 2020 that you might want to check out.

food utensils

Don’t like sharing utensils in the pantry? You can also store a set of reusable stainless eating utensils and straws in your locker for easy access.

locker hook

Add some hooks to your locker to hang your keys, umbrella, calendar or mirror. Look for ones with strong adhesive backing so they can withstand whatever you need to hang them on.

Magnetic pencil holder

If you have a metal locker in your office, opt for a magnetic pen holder that you can easily attach to the inside of your locker. Keep all your writing and organizational supplies in one place while maximizing your locker space.

Portable umbrella

For those rainy days – It’s always a good idea to keep a portable umbrella in your locker for those occasions. This is also a must if you use public transport to get to work, as there are times when you forget your umbrella at home.

duffel bag

The perfect place to store all your personal hygiene items such as deodorant, dental floss, toothbrush, etc.

Emergency Office Sweater

If you’re in an office whose temperature is set to permafrost, you might want to keep another sweater in there somewhere

water bottle/flask

We need to stay hydrated while we work now, right? Any type of water bottle will do, but if you want to keep your drinks fresher a little longer, you can use a vacuum insulated water bottle. Keeps your cold drinks cold and hot drinks hot, hour after hour.

It’s important to keep your office locker in tip-top shape, but want to know how you can do better? Speak to us today to learn more about our NS1000 lock and how it can help add value and security to your facility.

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