# Questions tagged [number-theory]

A mathematical puzzle whose solution is heavily based on the arithmetic properties of the integers. General number theory questions are off-topic but can be asked on Mathematics Stack Exchange.

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### Arrange (+,-,x,/) into the upsilon grid

Put operators $(+,-,×,/)$ into the squares. Each operator must appears exactly 3 times to make the operations correct. C is a constant. No BODMA rules ((×) and (/) is NOT HIGHER than (+) and (−)), do ...
384 views

### Arrange numbers 1 to 9 into the upsilon grid

Arrange numbers 1 to 9 into the octagon, so the operation is correct. C is a constant. Do the math operation in sequence, ($×$) and ($/$) is NOT HIGHER than ($+$) and ($-$).
387 views

### The pre-alpha calculator

You are given a rudimentary prototype of a calculator with only the following keys: 0 1 2 3 4 5 6 7 8 9 + - × ÷ = The display has place for 10 digits and is initially showing ...
2k views

### A Numbers Crossword

This is just a straightforward crossword puzzle. Every answer is some positive integer. To make it a bit more interesting I have withheld the clue for H5. Use the fact that with the clue for H5 the ...
154 views

### A bet with numbers between 1 and 24 [closed]

An urn contains 24 balls numbered 1 to 24. Three balls are removed from the urn. If you have to place a simultaneous bet for both the sum (S) and product (P) of those three numbers, what numbers would ...
499 views

### A Gathering of Number-Theorists

A certain number of the 5000 members of the World Arithmetical Society (each of which has a different membership number between 1 and 5000) got together to discuss a problem. Much to their surprise, ...
531 views

### Solve for three distinct digits A,B,C - no programming please

$A$, $B$ and $C$ are three distinct digits between 1 and 9 (not 0). What are they if: $A + B^2 + C^3 = ABC$ (need three solutions) $A + B^2 + C^3 = BAC$ (one solution) $A + B^2 + C^3 = ACB$ (one ...
373 views

### Another puzzle on the properties of the prime 2017

$2017$ is the first prime that satisfies the following three conditions: $p$ can be written as $a^2+21b^2$ for integers $a,b$; in this case, $2017=41^2+21\cdot 4^2$. $p$ can be written as $c^2+24d^2$...
314 views

### Help a man to recover his PIN

A man forgot his 6 digits PIN, but fortunately he remembered the clue for his PIN. The n-th digit is the first digit of (product of other digits multiplied by n) The number is not 000000 ...
726 views

### Arrange numbers to 3 different math operations

Replace letters with numbers 1 to 9, so the 3 operations below are equals. Each letter represents one unique number. $$\frac{ab}{c} = de \times f = gh - i$$
618 views

### Find the number from 10 statements

You are given the following ten statements and are asked to determine a particular number. At least one of statements 7 and 8 is true. This either is the first true or the first false ...
157 views

### Arrange numbers and operators to piano-keys

Let a # b = a*10 + b Example : 5 # 5 = 55 9.5 # 3 = 98 Arrange numbers 1 to 7 to each piano's-white-keys. Then arrange operators (+,-,x,/, and #) to each ...
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### Numbers at the corners of concentric squares (part 2)

Put 4 distinct 1-digit non-negative numbers (A, B, C, D) on every vertex of a rectangle. Then put the last digit of the product of 2 connected vertices at the sides of the rectangle. Create a ...
852 views

### Create a 5x5 Modulo Grid

Create a 5x5 grid. A1 A2 a3 a4 a5 B1 B2 b3 b4 b5 c1 c2 c3 c4 c5 d1 d2 d3 d4 d5 e1 e2 e3 e4 e5 Seed A1, A2, B1 and B2 with numbers that allow the grid to be ...
907 views

### Arrange the numbers 1 to 19 in the circles

O---o---O / \ / \ o o o o / \ / \ O---o---O---o---O \ / \ / o o o o \ / \ / O---o---O Arrange ...
184 views

1 + 2 = 3 1 + 4 = 3 16 + 4 = 11 4 + 4 = 7 5 + 4 = 6 5 + 2 = 10 6 + 2 = 10 2 + 2 = 7 8 + 10 = 5 4 + 10 = 4 5 + 10 = 4 3 + 10 = 5 81 + 7 = ? Hint Hint 2 What is ...
945 views

### How many lawn gnomes do I have? [closed]

I want to brag with the size of my lawn gnome collection to pick up ladies. To make it easier to count them, I've tried to put them into groups of 10, then groups of 5, then groups of 4, of 3 and ...
288 views

### Create a 3x3 table with a specific rule

Take 9 distinct numbers from [0 to 9], then put the numbers to a 3x3 table, so : Each cell = Last digit of (sum of 2 numbers in the same row of the cell + sum of 2 numbers in the same column of the ...
2k views

### Last Digit of Multiplications

I have 4 different 1 digit positive integer numbers $(a,b,c,d)$. than I apply this formula $random(a,b,c,d) × random(a,b,c,d) × ... × random(a,b,c,d)$ the last digit of the result is always one of ...
286 views

### 5x5 Table which number in every cell = last digit of (sum of its neighbor)

[1 . 6 . 7] [. . . 0 .] [3 . . . .] [. . . . 1] [. 7 . 8 .] fill the dots on the table above with 1 digit numbers, so: Number in every cell = last digit ...
254 views

### Curios observation about a special grid - Why?

[0,1,6,4,3] [4,5,6,0,9] [9,9,0,1,1] [1,0,4,5,6] [7,6,4,9,0] This 5x5 table has unique properties. Each number in a cell means : The cell = last digit of (sum ...
1k views

### We are 5 different numbers

We are 5 different positive integer numbers smaller than 100. The product of us is an odd number. The product of us is a cube number. The sum of us is a cube number. Determine what numbers we ...
2k views

### Ages of mathematician's five children

Two mathematicians meet at their school reunion. A: Hey old friend, I heard you have 5 children. How old are they? B: The sum of their ages is a cube number, A: But, I still don't know their ...
382 views

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### The oldest wins the prize, but they won't tell their age

I'm trying to design a problem that should be as close as possible to the following setup, while meeting some requirements about its solutions. Initial setup There is a group of more than 2 people ...
908 views

### Professor Halfbrain and the powers of 2016

Yesterday I met professor Halfbrain at the coffee house. The professor told me that he had been spending his time with computing powers of $2016$ and combining them with powers of $32$. The professor ...