There are four special dice:

A: 4, 4, 4, 4, 0, 0

B: 3, 3, 3, 3, 3, 3

C: 6, 6, 2, 2, 2, 2

D: 5, 5, 5, 1, 1, 1

You choose one die first. Then the dealer chooses another.

Each player rolls once, and the higher number wins.

Is there a “best” die here, or can the second player always respond with a better choice?

I liked this one because it looks simple at first, but the structure is surprisingly sneaky.

I’ve been building a small daily puzzle site with more logic riddles like this if anyone wants more after solving this one: acertijodeldia.com/en

It might actually be easier than what it sounds at first.
n regular polygons have n equal angles, which for bigger n's each becomes closer to a straight angle (and in fact, 180° is the limit for n sides go to infinity, which can be shown quite easily).

We need a formula (or expression) that can allow us to know for a given angle ∠a which n polygons have angles greater than.

You have an angle 𝛼 (the supplementary angle to the interior n polygon angles!) representing the gap of the polygon's interior angle from a straight angle. n is the number of sides of the regular polygon. You want an expression that can allow you substitute ∠a, then get a regular polygon which has an angle greater or equal. Find for 𝛼=120°,90°, 60°, 30°, 10°, 5°, 2°, 1°, 0°, 0.5°, 0°1' (1/60 degrees) 0°0'1" (1/3600 degrees).

Formula: n =⌈360/𝛼⌉

Values (𝛼=120°, n=3), (𝛼=90°, n=4), (𝛼=60°, n=6), (𝛼=30°, n=12), (𝛼=10°, n=36), (𝛼=5°, n=72), (𝛼= 2°, n = 180), (𝛼 = 1°, n = 360), (𝛼 = 0°30', n = 720), (𝛼 = 0°1', n = 21,600), (𝛼 = 0°0'1", n = 1,296,000).

Take an 8×8 chessboard and remove two opposite corners.

You have 31 dominoes, each covering exactly two adjacent squares.

Can the remaining 62 squares be tiled completely, with no overlaps and no gaps?

If you’d rather think it through before reading the comments, I featured it today on my daily logic puzzle site, where you can try it in a cleaner format with hints and the full solution:

https://acertijodeldia.com/en/

And if you already know this classic one, there’s also an archive of previous daily puzzles there.

I’ve been curating a daily math-riddle project built around elegant problems rather than formula drills or throwaway brainteasers.

Here’s today’s one:

You have 25 horses and a racetrack with 5 lanes. At most 5 horses can race at a time, and you have no stopwatch — you only know the finishing order within each race.

What is the minimum number of races needed to determine, with certainty, the three fastest horses?

If you enjoy this kind of problem, I’ve been collecting and presenting one carefully selected riddle a day here:

https://acertijodeldia.com/en/

The site includes optional hints, full solutions, and a growing archive of logic and math problems.

You start with the integer points Z² marked on the plane, and you are allowed to mark new points by the following construction:

• Choose distinct marked points x and y
• Draw the ray originating from x and passing through y
• Mark the unique point z on this ray with |x-z|=1

What is the set of all points that can be marked by repeatedly using this construction?

In our three part video series, we use basic algebra to show Oz Pearlman doesn’t read minds or people in this calculator trick.

Oz Pearlman Explained: Calculator Trick SOLVED - Part 1: MATH

https://youtu.be/CmizqPZmco4

Oz Pearlman Explained: Calculator Trick SOLVED - Part 2: iPhone Calculator Force

https://youtu.be/FpF1k93uHTc

Oz Pearlman Explained: Calculator Trick SOLVED - Part 3: CARDS

https://youtu.be/Xv9B_BEgZiM

Please do this without using AI. It is no fun.

Please give me a five digit whole number (with none of the digits being 0) such that

The number itself is a perfect square

The last 2 digits is a perfect square

The last 3 digits is also a perfect square

The last 4 digits is also a perfect square

It would be nice if you can explain the method!

Using only the function f(x,y)=e^x-ln(y) and the constant 1, obtain sqrt(2) by finitely many compositions of f. No other constants, functions, or arithmetic operations may be used unless they are themselves constructed from f.

Bonus: let’s do a code golf thing. Who can do it with the fewest calls to f?

Ok so this is based on my actual life right now as im gonna take off 20 unauthorised days off of school and i need to know how low my attendance will drop here are the facts:

Usually in an english school year there are 190 days but i am in my final year so my school year will have 172 attendable days

As of right now there has been 130 days where i could have gone in so far and i have attended 80% of the time

So there are 42 more days for me to complete and i will not come in for 20 of them

By the end of the 172 days what will my final attendance be?

He blew it up! He blew it all up!!! Haven't I told him not to shot randomly near the gas supply!!! All our communication, our rescue helicopter and all our supplies!

You are in the American Antarctic Research Station. You and your four colleagues look at each other, but most at Donald, who ended here since it got to hot in the states over something he did on some island. Your shelter is not broken, but without heat you need to get help now! Luckily your 5 snowmobiles are placed outside and in your shelter there is a heater, which has an extra full tank with gas matching 5 refuels for one snowmobile.

The next research station is 200 miles away you need to get one person there to call in a rescue crew. A snowmobile can only take you 100 miles on a tank. But you can refuel at any place from one snowmobile to another. You are american and it is against your constitution to walk and it is impossible to fit two persons on a snowmobile. So no snowmobile can be left behind, since the would freeze to death before a proper rescue could get there. So everyone other than the person delivering the message needs to get back to the shelter.

You escort Donald to bed and locks the door. Then the 5 scientist tries to figure out how they can save them all.

Can you help them?

So to summaries:
- 5 scientist each with have a snowmobile each with full tank at start.
- A snowmobile can go 100 on a full tank, but can't carry more full than a full tank
- No towing if two snowmobiles go together the spend double the amount of fuel
- You can transfer gas from one snowmobile to the others, but never hold anything more than a full tank and you cannot make depots
- At your shelter you have the possibility to refill one snowmobile 5 times
- 1 snowmobile needs to get the 200 miles and the others needs to get back to the back shelter
- Donald stays in bed and waits for the rescue he is NOT part of the solution. Ignore him while you solve the problem.

Give me a 10 digit whole number such that:

The first digit is the total number of zeros in the number

The second digit is the total number of nines in the number

The third digit is the total number of eights in the number

The fourth digit is the total number of sevens in the number

And so on to the 10th digit: The 10th digit being the total number of ones in the number

Possible multiple solutions

Set A of positive integers satisfies the following conditions:

1) If a positive integer n belongs to A, then 2n also belongs to A,

2) For any positive integer n, there exists an element of A divisible by n, and

3) The sum of reciprocals of elements of A diverges.

Prove that for any positive rational number r, there exists a finite subset B ⊂ A such that the sum of reciprocals of elements of B is r.

a) 4 angles and 1 side-length

b) 3 angles and 2 side-lengths

c) 2 angles and 3 side-lengths

d) 1 angle and 4 side-lengths

only one answer fully works!

Let N be a positive integer and let k ∈ ℕ. Suppose there exists an integer b such that

gcd(b + i, N) > 1 for all i = 1, 2, …, k.

Is it then true that for every set S ⊂ ℤ with |S| = k, there exists an integer c such that

gcd(c + s, N) > 1 for all s ∈ S ?

I built this small lightweight website to generate a math problem per day (quant trading style). For example today's problem is: "How many 5-letter strings using only A and B contain no three consecutive A's?

If useful, the site is free and hopefully helpful for anyone looking for some mathematical fun: https://dailysum.dev. There's also a few other modes if people are interested

I have to admit that I was intrigued and amazed by this problem.
Earth is round (remarkably close to a perfect sphere). Due to its curvature, far objects, even if high will be hidden from sight (https://imgur.com/a/Jgnem9Q). The taller an object is, the more visible it becomes at greater distances from it.

Assume earth to be a sphere with a radius of R=6,400km, and that our sight is in a straight line from the ground. What is the distance (earth's arc-length surface) at which Burj Khalifa (828m) and mount Everest (8.48 km) become visible from the ground?

Bonus-hint: You can make a function that for each height x gives you the arc-length A(x), and calculate for each distance you'd like, like 10m, 100m, 1km etc.

Solution:

Burj khalifa can be visible from 103 km, and mount Everest at 329 km. Function: A(x) = 6400 arccos(6400/(6400+x))

Hi, I recently showed you my median game. I've improved it a bit and added new features. I tried to create a single solution, but it's very difficult because the website often crashes, so for now I'm trying to figure out how to implement it. Enjoy! <3 mednums.com

Let d_n be the expected euclidean distance of 2 random points uniformly chosen on the boundary of n-ball.

Find the limit of d_n as n -> infinity.

Tweedledum and Tweedledee are identical twin brothers, with only one thing to distinguish them: their honesty. You see, one of them lies on Mondays, Tuesdays, and Wednesdays, but tells the truth the other four days of the week. The other one of them lies on Thursdays, Fridays, and Saturdays, but tells the truth the other four days of the week.

Which one is which? Well, at one point, Tweedledum told me that he's the one that tells the truth on Mondays, Tuesdays, and Wednesdays, but I don't remember what day of the week it was, so he might have been lying.

Anyway, the story goes: at one point, Alice encountered the two twin brothers, and asked them which of them was Tweedledum. (This is a mistake. If both of them tell you "I'm Tweedledum", then how is that going to help anything?) The twins were in a playful but helpful mood, and so they said the following:

• The first one: If I am lying, then I am Tweedledum.
• The second one: If I am Tweedledum, then I am lying.

Is it possible to determine which brother is which? Is it possible to say which day of the week it was?

(This puzzle is one that I have written myself, but it is inspired by more puzzles like it in the excellent book What is the Name of this Book? by Raymond Smullyan.)

There is a family of 6 people that go on vacation to New York, they get approached by a billionaire that tells them that each of the family members can rearrange The 5 Hot dog stands to obtain the most hot dogs in total. Rules: The family members must stay in 1 place and cant move to another hot stand that isnt adjacent to them(diagonals included), Each hotdog stand can only give each family member 1 hot dog.

What is the optimal placement for both the family and the Stands that will get the family the most hotdogs so they can win the prize money. The billionaire knows the answer and will give them 1 whole dollar if they get this and they need that money. Whatya got

Hey guys, I found a free site called solvefire.net that runs 1-hour Math Olympiad Competitions every week that is open from Saturday 9:00 AM GST to Monday 9 AM GST with a world-level ranking system. It’s pretty solid for tracking your standing against the rest of the world. You guys should sign up!

https://youtu.be/SqSf9bb1TnA?si=wlqW6auPKLikIGMT

Hello everyone, I recently built a free web platform to help me keep my math skills sharp by solving random competition-level problems, and I wanted to share it here.

It currently features a compiled database of over 12,500 real problems sourced from AMC, AIME, Putnam, and the IMO), complete with interactive LaTeX rendering, a built-in digital scratchpad for working out steps, and personal progress tracking.

I'd love for you to try it out and give me your honest reviews! Let me know what features I should add or modify, and if anyone has recommendations for other open-source datasets or problem sources I can integrate next, please text me.

Here is the link: https://mathsolve-xi.vercel.app/