I am a number.

break me apart. raise each up to itself as a power. take the sum, and build a tower.

back to the start, that tower is me! only 1 and I can claim this to be.

(but this doesn't work in base 3)

edit: still working on this one so to avoid further confusion please just avoid the word tower. i just meant the visual of a tower and it rhymed lol didn't think of the obvious tower reference to exponents

(Just shitposting related to this one: https://www.reddit.com/r/mathriddles/comments/ibjwsj/find_positive_integers_xyz_such_that_xyz_yxz_zxy_4/. Smallest solution I know of has 44 digits in the smallest number.)

Suppose you have two nonidentical triangles abc & def, where all of {a,b,c,d,e,f} are integers and {a,b,c}=/={k*d,k*e,k*f}, where k is rational. Show that, if one of the angles {A,B,C} is equal to one of the angles {D,E,F}, then the triangles are right triangles, and the right angles are the equal angles.

If I have 366 marbles in a box where half were green and half were red. Then what I did was keep adding 50 black marbles every time I take 2 green marbles, then what is the chance that I will get 10 red marbles in a row?

Edit: I can only take one marble each time I pick.

A math professor said to her smart student Toni

" I am thinking of a 4 digit prime number abcd (digits not necessarily distinct) with the following property

a+b+c+d = axbxcxd

You can ask me one question to which my answer can only be Yes or No or Silence (if i cannot definitely answer yes or no). Can you guess my number?"

Toni worked on a piece of paper and then asked the professor:

"Is the number formed by using the first two digits (in order) of your 4 digit prime, a factor of 63 or 84?"

The professor smiled. She knew Toni had the answer.

What was the answer? WHY?

Three men book a room total cost 30$. Each puts in ten. Mgr realizes should only be 25/night. Refunds 1$ each man, keeps 2 for self. So each paid 9$, manager kept 2. Three men at 9$ is 27.00. Mgr kept 2.00. 27+2=29. Where is the missing dollar?

A boy randomly colors every real point in [0;1] with a color y chosen uniformly at random in [0;1]. What is the probability that two points will share the same color ?

That's a trick question

For any 3 digit number:
ABC

Prove that
ABxBC=(ABCxB)+(10xAxC)

I hope you have fun solving it🙂

The problem isn't mine, but it's not very well known either.

A widget costs $1000. The store offers you a payment plan: pay $100 now, $100 in a month, ..., $100 in 10 months (total $1100). Estimate the annual interest rate of this payment plan.

I am a three digit number where the product of my digits equals my sum, my first digit is a prime, my second digit is a square, and my last digit is neither, yet I am the smallest of my kind. What am I?

Find the volume of an ice cream. It is composed of a cone and semisphere with the same circle circumference. The sphere's radius is r and the cone's radius and height are r, h respectively.

I have 14L of 57:1 Fuel and 9L of 30:1 Fuel - if I mix the two together, what is my new ratio?

Concentric circles are circles that share the same center point.

Imagine you have two lanes on a road. There are n cars in one of the lanes and k cars in the other lane. n > k. You are all waiting at a traffic light and you are in the lane with n cars. You have two options - either you can switch lanes and improve your position or you can wait for cars in your lane to switch and naturally improve your position in your current lane.

Should you switch lanes to improve your position or simply wait in your lane for other cars to switch?

I thought I'd post some of the most fun proofs I've seen so far in my math education for those who haven't seen them. These problems are aimed at math undergraduates and talented highschoolers. Those of you who have seen the answers, please avoid spoiling them!

Prove: The non-trivial zeroes of the Riemann zeta function all have real part 1/2.

Short, simple proofs are encouraged.

We got the sequence of n-regular polygons (starting with n=3):
n=3 is an equilateral triangle
n=4 is a square
n=5 is a regular pentagon
n=6 is a regular hexagon
etc....

Let the circumradius of the n-polygon be labeled as r and its apothem as a.

The question is to find the limit of the perimeter and the area of the n-polygon as n approaches infinity.

Hey there!

Couldn't figure that out. (Im translating it from different language, if there's something you dont understand feel free to ask)

There are 2 different printers in room, which of one printer prints 1.5 times more sheets than other one. It takes 45 minutes for the slower printer to print half of the request. How many minutes it takes for these 2 printers (working together) to fill the order/request.

Hey everyone,

I've got a puzzle for you to solve! Imagine you're in a maze with 4 rooms, each filled with gold, and you need to find the optimal route to exit with the most treasure possible. Here are the details:

You are in a maze with 4 rooms, each with gold inside. Room A has 40 gold, B has 50, C has 75, and D has 100.

Each room is connected via a Path that costs a certain amount of gold to use. To determine how much gold you need to pay, complete that Path’s math equation and deduct its result (rounding up) from your total gold.

The Path equations are as follows:

Pathway AB: 2 + 3 * 4 - 5 / 10 + 5^2

Pathway AC: 2^3 + 4 * 5 - 6 /10 + 1

Pathway BC: 5 * 4 - 2 + 5^2 - 7

Pathway BD: 3 + 4 * 5 - 8 / 2 + 1

Pathway CD: 3^3 + 8 - 5 * 3 + 8

Your total gold cannot be reduced below zero, gold can only be gained once per room, and Paths can be used from either direction. Assuming you start in room A and exit in room D, determine the optimal route through the rooms to exit with the most treasure possible.

Your final answer must be the order of the rooms visited (e.g., ABC, ABD, etc.).

The options are ABD, ACD, ABCD and ACBD

TL/DR: I think the answer is ACBD based on my approach, where you maximize your gold by visiting rooms in the order: A -> C -> B -> D. What do you think?

Costs: AB 38.5 AC 28.4 BC 36 BD 20 CD 28

Looking forward to seeing your solutions and insights! Thanks in advance!

Here is a better, harder version of this riddle.

https://www.reddit.com/r/mathriddles/s/CLCUUY0kVN

Tom orders a pillow online. His Mother likes it so much, she wants the same pillow for herself and her husband. She asked Tom how much it cost him and gave him double the money to order 2 more pillows. Tom orders 2 new pillows and gets to keep 5 dollars.

Toms mother lets Tom order 3 more pillows as a gift to her friends and gives Tom triple the money Tom spent the first time. Tom has now made exactly the same amount of money he spent the first time.

How much does one pillow cost?

Edit: Everything is constant. For example, price of 2 pillows is 2 times the price of 1 pillow.

This part is not needed but I'll add it anyways. Try to solve it without this part.

When Tom ordered 3 pillows, he kept double the money from when he ordered 2 pillows

Stranger walks into a Hat Store, wants to buy a hat for $10.00 and gives the Store Owner $25.00. The Store Owner does not have change for it. The Store Owner goes to the Flower Shop next door, asks to exchange $25.00. The Flower Shop Lady gives him $10.00, $10.00 and $5.00. Hat Store Owner goes back to his store and gives stranger his hat and $15.00 in change.

An hour latter the Flower Shop Lady come in and says that $25.00 he gave her is fake, so Hat Store Owner gives her $25.00 out of his register.

Question: How much money did the Hat Store Owner loose?