Hopscotch Programming Puzzles


Wow, thank you!

I have realized through the years that learning math at school is absolutely terrible.

A whole rant about why school and math don't go together

Most schools teach math in a very uninspiring way, a way that’ll make people feel like math is boring and a waste of time. However, there are some people, like me, who just love math. I don’t know why I started to love math, but I remember in Kindergarten being fascinated with areas of mathematics like multiplication and quadrillions and large numbers (Googology is a lot of fun, I used to to extremely interested in large numbers, and still am, and there’s a whole wiki about it! :smile:). I had heard of these things outside of school, outside of what they were teaching us. This kind of creates a curiousness and the natural love of math because you begin to descover, “Woah. There’s a LOT more out there than what is being taught at school.” School kind of shows the tip of the ice burg of mathematics, but they do it in such an uninspiring way that most kids never want to find out the hidden mysteries underneath. That is why it is crucial that if you want to learn math, be good at it, and have fun with it, you must do it in you’re own time

I have been some Khan Academy, I realized that I could do trig over the summer, but a lot of it was review in a way, and I also really despise the videos. They are really boring. I did find a section of math in Khan, but at the very end of the math journey. It’s called, “Math for fun and glory”. They only show videos and it’s a lot of fun, I definitely would recommend it (I must admit I would’ve been even more excited about it a year or 2 ago since I’ve learned the math topics by watching things like Numberphile) (Also, they bring on a different person, I forget her name, but she does actual drawing with a marker on lined paper. It is absolutely glorious).

Yeah, I had realized that very quickly when I decided that math had become my life. However, without a core study place, you have no 100% proof that your actually going to find a place where you can learn math that is fun and easy (Especially for topics like calculus and abstract algebra and higher dimensional math – which is an absolute bummer because these subjects are so fascinating).

Throughout that past year, I have been watching Numberphile very thouroughly. I also found a new YouTube channel called 3Blue1Brown that teaches many things like calculus. I had also been able to collect some books to make a mathematical bookshelf, which I am very excited about. (Some of my favorites were, Hyperspace (when looking online for it, type: Hyperspace (book) ), What to make and do in the 4th dimension, and Ian Stewart’s mathematical cabinet (And also “What if?” by xkcd).

I have also realized that math and science literally go hand in hand, which is a whole new thing

Woah, I’ve typed a lot, I get really excited about math when I’m able to talk about it with people who have the same kind of passion for it, thank you so much!

Also, I created a topic here on the forum a few weeks ago that show math recourses people can use, I’m probably going to fix it up and add some more. I think it is a great idea so that people who are bored in school can find amazing ways to learn (The girl who talks in the “Math for fun and glory” even admits that school math is boring, she just doodles all class about more interesting parts of math (hehe, I did that in my Algebra 2 class, but I probably should have.)



I so agree with your rant on math + school. its just skill and drill and stuff to bore you out of your mind. last year my teachers didn’t know what to do with me so they just shoved me in the back of the classroom and made me do John Hopkins University online courses, which i did well on, but it was soooo boring.

idk what kind of calc you’re doing but AoPS (Art of Problem Solving) has a really great book on it (you might be beyond it’s level), but it’s written by people who’ve competed in the math Olympiads (which is really hard and basically the Olympics for math). I highly suggest it. [Calc Book] Cause the material in there is definitely not skill and drill and really furthers your understanding. they put like math competition problems in there which makes it really fun.

AoPS also has a great forum. I have never felt so dumb in my life after seeing sixth graders learning what I’m learning now. the forum houses some of the smartest kids. a good portion of the kids who go to the Math Olympiads are on this forum. anyways, it’s really good. you can find me as math.fever (my status is “Queen”) tho i never really use it.


Yes, thank you! My mom and I have just recently learned about the AoPS and AMC program! (No, I’m not officially in calculus yet, but that doesn’t stop me from trying to find awesome stuff all over the web)

I will definitely check out the math.fever and go onto the AoPS forum, thank you so much for suggesting them!

I really dislike the skill/drill stuff from school and shoving everything in your mind through boring lectures only to regurgitate it onto tests and then forgetting everything a few minutes later. It really stinks. It’s a bummer that every singe school is like that.
(The school I went to last year puffed themselves up saying they were the best and incredible and all that jazz, but the teachers were just uninspiring and it was lame. A huge let down. That’s why I’ve been trying to scavenge through the internet finding anything, because learning and discovering things by yourself is absolutely great for learning)

Ugh I’m off on a rant again, sorry :joy:

Meanwhile, if I actually end up finishing this post, I will definetely give the links a try, thanks again!

It just so happens that I already have the trig and precalc AoPS books at my house! I am definitely going to order the calculus one very soon (I think we also have the number theory one and also geometry and algebra for my siblings). We’ve been starting to use AoPS (probably also because this’ll be my first year of homeschooling) and it has been a great resource! – also the AMC is like a math competition that’s associated with AoPS and I’ve heard from my friends that it is really great


Omg my teachers are extremely boring. And they tell you not to go ahead of the class? Like, I thought you were supposed to encourage us to learn?? Every time I see a math topic on here I feel. so. dumb. Texas is the 26th rated state for math curriculum/student grades. And the U.S was like the 36th country (although that’s outdated bc that is info from 2012. The Texas thing is from 2017 though) So, that means Texas is pretty behind compared to the rest of the world.


But Texas has good tacos.


And pizza.


Hey, that’s cool, Minnesota is in the top 3! I used to live there, the public schools were superb. It was a great expirience until I moved to the Bay Area CA back in 2011. The schools here are uninspiring, despite the vastly growing tech city

I’m also not surprised California is at the bottom 45. Terrible. Utterly terrible


I’m going into high school this school year and they’re making me take AB calc which means i’ll be sitting with a bunch of juniors/seniors and idk how to feel about it. :joy:

I also recommend the AoPS online classes. No videos. It’s live, typically at night and you have a chance to interact with your instructor. There’s like 60-70 kids per class. the classes are basically like a large online group chat. anyways, i wouldn’t take the courses without a good understanding of the basics of calc or else you may as well cry (as i did when i was ten and my mom made me do the intro to counting/probability course). it’s challenging, but i say pretty fun.

@Intellection74 my old school was pretty good to me. like the teachers were too dumb to teach me so they set me up with the “best” online course. and it was boring but i had to do it since my school paid like $4,000 for it which was pretty nice.
also, this year, the US won 1st at the math Olympiads (so US is very smart. even china placed second and china always wins), and 7th grader Luke Robitaille from texas took first place at Mathcounts Nationals, Andrew Kai (also texas) took second, and overall Texas placed first at Mathcounts Nationals. Texas is definitely one of the smartest states. it has a large population which could be one of the reasons why it’s a bit behind.

@JonnyGamer yeah. I’ve taken the AMC 8 since 6th grade, although I failed miserably this year, made four silly mistakes and only got a score of 21/25. And last year I took the AMC 10A and 10B. The score which i received we shall not talk about. but this year I took the AMC 10A (shall not talk about score) and 12B (96.5pts) and MISSED THE FREAKING CUTOFF BY 4 POINTS!!!


Sorry, this was the only place I could contact
How 2 make groups?


Ok, awesome, I should probably read a book or 2 on it (or probably the actual AoPS book). I just completed Algebra 2 and I learned nearly all of Trig on Khan Academy, but I have not whatsoever touched Pre Calc yet. I was shown the completion quiz of trig/precalc, which was neat, but I am not too sure if I’d be able to understand the calc class yet. (I hear calculus is just an advanced version of Algebra + Geometry + Alg.2 + Trig + PreCalc shoved into one awesome course. So learning and mastering the basics of all these subjects are most likely crucial) (I also found a YouTube series on Calculus made by 3Blue1Brown that I’m going to be watching really soon, that’s probably going to be a big help)

So my main question is whether or not the AoPS group chat lessons are any good or not. I see that you need to have a huge understanding in the subject (this reminds me of Stories my friends told me about the AMC how the questions get progressively harder really fast). So I’m kind of scared and nervous, but also really excited about it!

– Oh! I’ve seen you added more to your post

I haven’t taken an AMC before but ive heard the final questions are near impossible and require much more brain thinking than 75 minutes (the final questions taking 15 mins to complete each)


Saw u liked this, do u know how?


Yeah, there’s a topic about it that t1 made, she’s the only one who can create them, here’s a link to the topic, you also have to fill out the form about what the group is about


I have an awesome puzzle I’d like to share with everyone! It’s more about math, though, so there’s no need to program it.

The Four 4’s:

This is a game called the Four 4’s. It is a challenging math game that increases in difficulty as you go along.

The goal of the game is to make every single whole number, using only four 4’s, and an unlimited about of mathematical symbols.

Here’s is an example:

1: (4 + 4)/(4 + 4)

The 4’s that you can use are 4, .4, and .4 repeating.

Allowed symbols to use

Don’t use the reciprocal symbol yet.

My record is straight until 143 (143 is really tricky). I needed the reciprocal notation to solve 103, 109, and 134 though.

This is an awesome mathy challenge, I hope you all like it! (It’s really addicting and a lot of fun)


Oh, cool, I’m going to try this :smiley:


I challenge you to make the largest number possible with this game and imma see if I can find a larger one. You can leave it in its notation.

Anyone can try this Tho


143 = (4!^√4 - 4) / 4 … I think xD

@Kiwicute2013 I’m cheaty, but I know I have you beat. First, define A(x,y) as the Ackermann Function, which is the fastest growing function ever used in a mathematical paper (A(4, 2) is around 2×10^19728). Then, define G as Grahams number, the largest number ever used in a mathematical paper. Then:

Where ln is natural log. It’s impossible to grasp how unfathomably large this number is, but to give you as good of an idea as you can, lets say you took all the atoms in the universe. Call the number of atoms in the universe X. Then, let’s say every single atom of the universe had a copy of our universe inside it, and every atom in each of those universes had a copy of the universe inside it, and so on X times. Add up the number of atoms in all those universes, and you have made it… 0.0000000000000…000001% of the way to our number. And here’s the killer - the number of 0s in that percentage is more than the sum of the atoms in all those universes.


No way. You just solved it like no problem, wow! Thanks!

That one was hiding in plain sight, wow :flushed:


Actually, I can create a number infinitely large.
Ex) (((((4!)!)!)!)!!!..



A good problem, though is to find the largest prime number. Primes are a real challenge in this game


My program solved it, not me :stuck_out_tongue:

113 is impossible for me, can you figure it out?


I have solved that one, I need to find my booklet, though
The ones above 100 are super difficult

Here we go:
I specifically remember this tricky one

113 = (4^4 * (4/9) ) - (2/3)

4/9 = point four repeating
2/3 = the square root of point four repeating

The Numberphile Topic -- The Official Nerdy Math Topic! [OLD]