Supposed you are given the following numbers:
6
28
496
8128
33550336
8589869056
What's the relation between them?
This was inspired by many puzzles that use three/four numbers to create other numbers. I chose these numbers in particular because of this post.
Can you find a way to make all the natural numbers ...
Can you find a way to make:
$0\ 0 \ 0 \ 0 = 8$
by adding any operations or symbols? You can use only these symbols:
$+,\ ,\ *,\ !,\ /,\ \hat\, ,\ ()$.
It is limited to this list, and ...
Can you find a way to make:
6 5 4 3 = 1
by concatenation and/or adding any of (and only) these mathematical operators:
+

×
!
÷
^
standard parentheses ()
You cannot add other numbers to the ...
Inspired by Interview Question or Pathbreaking puzzle and A121808.
Start with $1$, and count the number of times $1$ occurs, and report this in the format 'number of ones:1', i.e. the next term is $...
Using the same rules as Make 6 5 4 3 = 1, but maximize the number of factorials. You may not take the factorial of 1 or 2.
This is harder than it looks. A great answer has six factorials, an ...
Can you find a way to make:
6 5 4 3 = 81
by concatenation and/or adding any of (and only) these mathematical operators:
+

×
!
÷
^
standard parentheses ()
You cannot add other numbers to the ...
Can you find a way to make:
$5\ 5 \ 5 \ 5 = 19$
by adding any operations or symbols? You can use only these symbols:
$+,\ ,\ *,\ !,\ /,\ \hat\, ,\ ()$.
It is limited to this list, and ...
$4+5=9$
$7+9=13$
$115=9$
$17+29=\,?$
Find the value of "?"
I am X. I was roaming around some place and found another X. We got attracted. Got into some operation and generate Y.
Me and my X got together now and went to roam the places.
We found the group ...
$A^2$ + $B^2$, $AB$, and $A + B$ are all integers.
Do both $A$ and $B$ have to be integers? If not, what is an example where they are not?
During a tournament, seven football teams, three European, three South American, and one from Africa, scored a total of 89 goals.
The number of goals scored by the African squad was relatively prime ...
The sum of nine whole numbers is 1000. If those numbers are placed on the vertices of this graph, two of them will be joined by an edge if and only if they have a common divisor greater than 1 (i.e. ...
Place the 18 even integers between 2 and 36 in the empty nodes of this triangular graph in such a way that if a path is drawn by coloring in red all the edges joining any two nodes whose numbers add ...
I'm trying to figure out what number follows next in this sequence. Can you help me?
5, 21, 341, 5461, 1398101, 22369621
The sum of the ages of six sisters known to me is 92. Though there is no single whole number greater than 1 that simultaneously divides the ages of any three of them, I did notice this morning, while ...
Four marathon runners, each identified with a positive whole number, sit around a table. Each of them notices that their own number has a common divisor with the number of the runner sitting on his ...
This is very similar to the 2, 0, 1, 8 problem. Just try to make all numbers 130 using the digits 2, 0, 1, 9.
Rules:
Use all four digits exactly once
Allowed operations: +, , x, ÷, ! (factorial), ...
We know that $23$ is a prime number nonetheless, I'm asking to find 4 numbers $a,b,c,d > 0$ such that $23$ factors.
$$ 23 = A \times B \times C \times D \text{ with } A,B,C,D = a + b \sqrt{2} + c \...
In the annual meeting of the International Conference of Puzzle Scenarios, each of $100$ people in a room is given a different number from the set $\{1!,2!,3!,...,99!,100!\}$. One person leaves the ...
This puzzle replaces all numbers with other symbols.
Your job, as the title suggests, is to find what number fits in the place of $\bigstar$.
All symbols abide to the following rules:
Each symbol ...
A maths teacher writes a very large number on the blackboard and asks her pupils (of whom there are $n$ in the room) about its factors.
The first pupil says, "The number is divisible by 2."
The ...
Find six positive natural numbers, not necessarily distinct, whose sum is 1000 and which, if placed appropriately on the vertices of the following graph, two of them will be joined by an edge if and ...
Label the vertices of this graph with positive integers (repetitions allowed) whose sum is 100 in such a way that any pair of vertices are joined by an edge if (and only if) they have labels with a ...
Captain Etarip, wants to plunder all the treasure islands that he can. There is exactly one island for every $n\in\mathbb N$. The $n^{\text{th}}$ treasure island contains three cities, each with $n$ ...
To create my puzzles, I often use the numerical properties of the integers. However, as of recently, I feel like I am running out of properties to use.
So, why not make it a sort of game to find ...
I'm currently working on a (difficult) number progression and need your help. How would you continue?
2, 5, 12, 25, 54, 113, 240, 481 ?
Thanks in forward!
Consider the following pixel puzzle which somehow looks like a damaged QR Code with clues on the left of every row and on the top of every column.
These numbers represent the total amount of "black ...
Imagine you have 2 types of chocolates (A and B). You randomly pick up two chocolates at once from your bag in a specific pattern. If the same type of chocolates come out, you give them both to your ...
This puzzle replaces all numbers with other symbols.
Your job, as the title suggests, is to find what value fits in the place of $\bigstar$. To get the basic idea down, I recommend you solve Puzzle 1 ...
This puzzle replaces all numbers with other symbols.
Your job, as the title suggests, is to find what value fits in the place of $\bigstar$. To get the basic idea down, I recommend you solve Puzzle 1 ...
Find the largest set of stricly positive integer terms in which none divides another and respecting the following rule: given any three of them, one divides the sum of the other two.
Source: ...
A teacher wrote a large number on the board and asked the students to tell about the divisors of the number one by one.
The 1st student said, "The number is divisible by 2."
The 2nd student said, "...
I just found this awesome puzzle from the Tournament of the Towns (though I'm sure it's appeared other places too). The connection between odd factors and square is surprising, and the proof has a ...
This puzzle replaces all numbers with other symbols.
Your job, as the title suggests, is to find what value fits in the place of $\bigstar$. To get the basic idea down, I recommend you solve Puzzle 1 ...
This puzzle replaces all numbers (and operations) with other symbols.
Your job, as the title suggests, is to find what value fits in the place of $\bigstar$.
All symbols abide to the following rules:...
Inspired by this puzzle : Integers around a circle with consecutive pairs adding to a square
The integers 1 to 50 are placed around a circle in such a way that the difference of any two of them which ...
This puzzle replaces all numbers (and operations) with other symbols.
Your job, as the title suggests, is to find what value fits in the place of $\bigstar$.
All symbols abide to the following rules:...
This puzzle replaces all numbers with other symbols.
Your job, as the title suggests, is to find what number fits in the place of $\bigstar$.
All symbols abide to the following rules:
Each symbol ...
This puzzle replaces all numbers with other symbols.
Your job, as the title suggests, is to find what number fits in the place of $\bigstar$.
All symbols abide to the following rules:
Each symbol ...
This puzzle replaces all numbers with other symbols.
Your job, as the title suggests, is to find what number fits in the place of $\bigstar$.
All symbols abide to the following rules:
Each symbol ...
Given a multiset of positive integers, its Pgraph is the loopless graph whose vertex set consists of those integers, any two of which are joined by an edge if they have a common divisor greater than ...
You are on vacation in New York City. You didn't bring your car, and it's currently around $50^\circ C$, so it's probably a good idea to take the NYC metro subway to move around.
You need a metro ...
I´ve forgotten my PIN, a fourdigit number. All I remember is that it is a perfect square, and that it has at least one digit in common with every other fourdigit square number. What is it?
The sum of the ages of my five daughters is 43. The ages of any two of them have a common factor greater than 1. How old are my daughters?
The sum of six positive integers is 200. If placed appropriately on the vertices of this graph, two of them will be joined by an edge if, and only if, they are not relatively prime, that is, if they ...
The sum of three positive integers is 120. Pairwise, exactly once (out of three possible pairs) are the numbers relatively prime (i.e. they have no common divisor greater than 1). What are the three ...
It has been shown that the smallest integer, greater than 1, that cannot be represented as a sum of two squares and at most two powers of 2 is 535,903. Show how to express 535,902 as the sum of two ...
We choose some numbers from the set $\{1, 2, ..., 100\}$.
What is the largest possible number of numbers from the set that can be chosen so that no two of the chosen numbers vary by 2 or 5?
The integers 1 to 50 are placed around a circle in such a way that the sum of any two of them which are adjacent is a perfect square. Of these integers, all but the prime integers were removed. ...