Questions tagged [primes]
A puzzle that involves and requires knowledge of prime numbers. Use with [mathematics]
57
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Covering a room with 34 carpets
There are 34 rectangular integers less than 100 which are the product of two primes. Can a room be covered precisely (no overlaps, etc.) with the 34 rectangles that have as areas these products?
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My library membership number
My library membership number, which I readily forget, is a 10-digit number, all different digits. However, I do remember it is the largest such number in which any block of four adjacent digits is ...
- 16.3k
4
votes
1
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More stepping stones
Start by placing prime numbers 2, 3 and 5 anywhere on an infinite square grid. Now you can place a prime number $p$ subject to the following rules:
It must be greater than all the previous numbers ...
- 28.8k
3
votes
2
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Using Prime numbers to get 100 and 1000
Using the digits 1 to 9 exactly once create a set of one or two digit prime numbers.
Use those prime numbers and the math operations + - / * and
parantheses to get 100.
Then use those exact same ...
- 39k
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Planar Investigator
Use logical deduction to place a different digit from 1 to 9 in each circle below so that 8 of the arrows form the primes 23, 31, 41, 53, 59, 79, 89, and 97. (We view an arrow starting at digit A and ...
- 15.3k
4
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A prime time traveler
It is the year 2140 and you have just turned 40. After years of research, you have finally invented the time machine! It is a small device that fits in your pocket and allows you to travel in time. ...
- 28.8k
2
votes
2
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Prime sums in a 3x3 grid version 2
Can you place the first 9 natural numbers (1 to 9) in a 3x3 grid such that every row and column sums to a prime? The sums do not need to be distinct. Bonus: can you also make both diagonals sum to a ...
- 28.8k
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Prime sums in a 3x3 grid
Can you place the first 9 odd primes in a 3x3 grid such that every row, column and both diagonals sum to a prime? The sums do not need to be distinct.
- 28.8k
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Scrabble with prime numbers!
How to Play
Overall, gameplay is very similar to typical Scrabble; however, unlike typical Scrabble, you'll be using digits instead of letters (we'll cover your tile bag later). The objective is to ...
- 10.5k
7
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Another Rook's Tour of the Chessboard
Place numbers 1 to 64 in the cells of this 8 x 8 board in such a way that consecutive numbers occupy neighboring cells (either vertically or horizontally). Shaded cells must be occupied by prime ...
- 16.3k
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Splitting the Primes
Is it possible to split the 25 primes less than 100 into two disjoint sets such that the sum of the primes in one set equals the product of the primes in the other set?
If so, in how many ways can ...
- 16.3k
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A King's Short Walk
Place the numbers 1 to 25 on the cells of this board so that any two consecutive numbers occupy cells that are horizontally, vertically or diagonally adjacent. Prime numbers should occupy shaded cells....
- 16.3k
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Squares and chords in a circle
The whole numbers 1 to 2n are placed in order around a circle. For which n is it possible to draw n non-intersecting chords (one from each number) such that each of them joins two numbers whose sum ...
- 16.3k
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Find an integer where each sum of 5 consecutive digits is prime
Find the largest positive integer with the following properties:
every sum of 5 neighboring digits in its decimal representation is a prime number.
those prime numbers get smaller and smaller from ...
- 11.8k
3
votes
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Magic Square Primes At Most
Take 9 numbers from 1~20 without repetition and fill them in a 3x3 grid so that the sums on each row, each column, and each diagonal are the same. If there are a primes among these 9 numbers at most, ...
- 31
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Trees from integers [closed]
A set of distinct positive integers is said to be a prime tree of integers if the graph obtained by letting the integers be its vertices, two of which are joined by an edge if (and only if) their sum ...
- 16.3k
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Primes and squares in a grid
i) Place thirteen different three-digit prime numbers in the empty cells of this grid.
ii) Now place thirteen different three-digit square numbers in the empty cells of this grid.
How many solutions ...
- 16.3k
2
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1
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Number conversion via Prime route
This is a variation of the Word Ladder. Instead this is a number ladder.
Convert the number 12345 to the number 54321 in seven or less steps
with the following rules
A: You can only change any one ...
- 39k
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votes
3
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Is this Prime Sequence the longest?
So you are interested in Prime Numbers and puzzles thereof. You saw the following on PSE and gave it a try and got it long after the correct answer was posted by @hexomino.
My Eight Cousins
But then ...
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votes
1
answer
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My Eight Cousins
My eight cousins are all a different prime number of years old, and their average age is a whole number. Recently they all came to visit me and, as they left one by one, I noticed that at all times ...
- 16.3k
1
vote
2
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Dividing the first 10 primes into groups whose sum is prime [closed]
Take the first 10 primes. Can you divide them into $g$ disjoint groups, such that the sum of numbers in each group is prime. In particular can you make this work for every value of $g$ in the range $[...
- 28.8k
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A number built with two-digit primes
What is the largest number, which can built as a sequence (from left to right) of different two-digit primes only?
For example, 1371731 is valid, 137131 is invalid (containing 13 twice), 139717 is ...
- 11.8k
6
votes
4
answers
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8x8 square with no adjacent numbers summing to a prime
Can you fill a 8x8 grid with numbers from 1 to 8 such that:
Every number occurs exactly once in each row and in each column (Latin square).
No two adjacent (horizontally or vertically) numbers sum to ...
- 28.8k
4
votes
1
answer
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Solving Kordemsky's Prime Cryptarithm and proving uniqueness
This is a cryptarithm from Kordemsky's The Moscow Puzzles, problem 273 to be precise. Each digit is a single-digit prime ($2,3,5,$ or $7$). Find a solution and prove that it is unique.
$$\begin{array}{...
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More primes and squares, in a summation triangle
Place a different prime number or perfect square in each of the twenty-one
disks that make up the triangle below, so that the number in any disk
that lies on two others is precisely the sum of the ...
- 16.3k
11
votes
2
answers
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Time... to be prime?
A standard analogue clock face has numbers 1 to 12 around the edge arranged sequentially, which is nice for telling the time, but not especially interesting. It is possible to arrange the numbers in ...
- 327
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2
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Prime stepping stones
Start by placing number $1$ anywhere on an infinite square grid. Now place numbers $2, 3, 4, \ldots, K$ in order. A number $k$ can be placed if the following rules hold:
It must be adjacent (...
- 28.8k
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votes
0
answers
292
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Even and primes puzzle?
These are secret numbers that increase regularly. What are the next two numbers?
If you like numbers, it will be fun.
$2^3 \times224299$
$2^2 \times 3^2 \times 19 \times 3557$
$2 \times 5 \times ...
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votes
1
answer
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My Latest Password
-What is your password?- my niece asks me.
-It is a four digit number.
-I know that.
-It is divisible by precisely three primes.
-Tell me more.
-It has at least one common divisor greater than 1 with ...
- 16.3k
6
votes
3
answers
353
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A Kind of Unique Prime Number
A Prime number with the following properties
Less than 7 digits and more than 3 digits
ALL digits in the number are Prime numbers-- some repeated.
All individual digits in the number add up to a ...
- 39k
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On certain triplets of consecutive integers [closed]
While completelely factorizing integers, my student Luciana noticed that the canonical prime factorization of the three consecutive numbers 81=3^4, 82=2x41, and 83=83, use numbers which are all ...
- 16.3k
13
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1
answer
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Gaby's Puzzle (Primes Around a Circle)
To keep them busy during lockdown, Gaby asked her children to find a way to place the first sixteen primes (2 to 53) around a circle so that either the sum or difference (or both) of any two of them ...
- 16.3k
6
votes
2
answers
424
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Primes in a Line
Place the first 20 primes (2 to 71) in a line so that the sum or difference (or both) of any two primes that find themselves next to each other is always a perfect square.
For which other values of N ...
- 16.3k
3
votes
1
answer
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Follow the path of relation through the grid #8
There is a relation between rectilinear-adjacent squares such that there is a unique rectilinear path from the top-left corner of the grid down to the bottom-right corner of the grid. Each square can ...
- 2,270
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Follow the path of relation through the grid #7
There is a relation between rectilinear-adjacent squares such that there is a unique rectilinear path from the top-left corner of the grid down to the bottom-right corner of the grid. Each square can ...
- 2,270
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Prime to number conversion
This puzzle relates to Prime to Prime: Get all first 25 Prime Numbers using up to 4 Primes and its sequel Prime to Prime Sequel
Using any three of the first 4 prime numbers (2,3,5 and 7) and the
...
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Can you cut through the mist?
I've created a mapping between words and complex-valued polynomials, and I've generated examples from word lists that I've I found on another puzzle. You don't need to study every one of these, but I ...
- 2,270
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votes
6
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A looped building with Prime rooms lighted
Imagine a building with 200 consecutive connected rooms as shown below. The shape is not important. It could be a circular loop building.
You do not know the room numbers but you are told that they ...
- 39k
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2
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It's my sister's birthday
I'd ordered her a cake, but when I got to the bakery to pick it up, the cake decorator had transposed the digits of her age.
"She'll thank you for the compliment," I said, "but her age is a prime ...
- 4,873
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A King's Hamiltonian Tours
a) Place the numbers 1 to 25 in the cells of a 5 x 5 board in such a way that consecutive numbers occur in adjacent cells either vertically, horizontally, or diagonally, and so do cells with numbers 1 ...
- 16.3k
20
votes
1
answer
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Prime number snake (2)
This question is inspired by prime number snake. In the following grid,
you have to place a number snake of numbers 1 to 100. Consecutive numbers have to go into neighboring cells.
Numbers in grey ...
- 2,124
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votes
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answers
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Prime Number Snake
Place numbers 1 to 100 in the cells of the 10 x 10 board below in such a way that consecutive numbers occupy neighboring cells (either horizontally or vertically). Shaded cells should contain only ...
- 16.3k
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votes
1
answer
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Living in prime years
A human was born somewhere in interval of [1;1920] A.D. They lived exactly 100 years. They lived through more years that were prime numbers than any other human (of the same lifespan) who was born in ...
- 458
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Reconstructing the results of a 6-team soccer tournament
6 teams played in a "round-robin" soccer tournament, in which each team played each other team once. Each game had 3 possible outcomes: team 1 won, draw, or team 2 won. The winning team received 3 ...
- 28.8k
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votes
1
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Prime to Prime Sequel
This question is inspired by the Prime to Prime puzzle.
The first 24 Prime Numbers are
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89
Using up to 4 prime ...
- 130k
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Prime to Prime: Get all first 25 Prime Numbers using up to 4 Primes
The first 25 Prime Numbers are
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97
Using up to 4 prime numbers and the following mathematical operations, get all the 25 primes.
+ ...
- 39k
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Prime parallel rows for the first 20 numbers
Two positive integers can be joined with a straight segment if their sum is a prime and the segment doesn't intersect any other segments. What is the most number of pairs you can join if you can place ...
- 28.8k
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1
answer
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The first 10 prime butterflies
A prime butterfly is a set of three distinct numbers $a,b,c$, such that $a+b$ and $b+c$ are both primes. Can you divide numbers from 1 to 30 into 10 prime butterflies?
- 28.8k
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Two equal-sized lists that produce prime sums
Place one or more distinct numbers between 1 and 100 into the lists $𝑃$ and $𝑄$, such that they contain the same number of elements and any number from $𝑃$ added to any number from $𝑄$ gives a ...
- 28.8k
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votes
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Dividing the first 20 numbers into 3 lists
Place every number from 1 to 20 into one of three lists $P$, $Q$ or $O$, such that any number from $P$ added to any number from $Q$ gives a prime. What is the fewest number of elements that can be in $...
- 28.8k