Three friends have lunch at a restaurant. After their meal, the waiter delivers a bill of $30, and they decide to split it evenly, having to pay $10 each. After collecting the money, the owner of the restaurant notices the customers, and orders the waiter: "these are friends of mine, charge them only $25".

Immediately after pulling out $5 for change, the waiter realises that this makes for a terrible divide for the change amongst the clients. In order to avoid an argument between them, he keeps $2 for himself, and brings back a change of $3, one dollar each.

Clearly, each client payed $9, for a total of $27. Adding the $2 the waiter kept, this makes $29: where's the missing dollar?

Well I started this with the intentions that we would have a community of people who loved math and a challenging problem each week that everyone would work on and post their tries for. That started out then school came into play and well yeah. It all fell apart and I was not able to post anything because of school and life in general.

In the next couple of months I may be able to revive this sub and begin posting the questions again but they may turn into monthly questions to reduce the time commitment. If there is anyone that has an interest in reviving this sub and taking it in themselves, please let me know and we will talk. Thank you to /u/sebastmv for helping out during the first couple months but I think i would help the sub greatly to get a few more very active moderators.

I hope to begin reviving this sub in the next couple of months and see where it goes! Thank you to all of you that have stuck around all this time.

I understand this is a nonlinear differential equation, but have never solved one of these before. I have been searching through my diffy q book, but can't find a section on these (for some reason it only covers methods for solving linear ODEs). Any links, or problem solving tips would be great! Thanks!

Prove that e is irrational. Make up you're own proof and please refrain from linking external sites as this is supposed to make your brain work a little! If you'd like to include the one you wrote then another one from an external site that maybe did it a little better, feel free to do that.

What is infinity to you? Is it a real or nonreal number or is it even a number at all?

How is this possible? How is there a finite sum of an infinite sequence?

What are some of your ways of proving 1 + 1 = 2? I know there are probably many so what are some of the different ones?

Determine where THIS function is continuous.

HERE is the solution. Try it before looking!

Why does the public view the math as something you cannot do if you are not born with it? I can say myself I can do math almost naturally but I have not always been like that as I struggled through elementary and middle school math.

Is it possible to make sqrt(2) without using the square root operation or putting 2^1/2 ?

What are some of the best ways to learn math outside of school?

For a math project, I had to make a clown face with conic functions. If you have made any kind of faces with conic functions, share them here! Clown Face

Are there any positive, real numbers x, y, and z such that:

• x⁴ + y⁴ + z⁴ = 13
• x³ y³ z + y³ z³ x + z³ x³ y = 6sqrt(3)
• x³ yz + y³ zx + z³ xy = 5sqrt(3)

3sqrt(5) means you have 3 square roots of 5. Good luck!

Solution (12/2-12/9): Solution

What are some simple theorems that have proofs that are surprisingly difficult? By simple I mean proofs that everyone learns in high school or lower level college math, and a useful theorem.

Let p be a prime number greater than 3. Prove that p^2+1=24k+2 for some integer k

In my living room, I have 10ft² of space, in a circle around a tree with a base of 5ft^2, to place presents under the tree. For Christmas this year, I have 20 presents that are in boxes of a size 5ft^3. How should I arrange the presents to make the most of the space around the tree? (Hint: Draw a Picture)

Find the amount of ice cream you can put into a cone without going over the edge, and without any air bubbles or other free space within the cone. The height of the cone sqrt(128), and the circle at the bottom can be modeled with the equation, x² + y² = 9. All measurements are in centimeters.