Questions tagged [primes]

A puzzle that involves and requires knowledge of prime numbers. Use with [mathematics]

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15
votes
2answers
1k views

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 ...
7
votes
2answers
403 views

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 ...
10
votes
2answers
572 views

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 ...
5
votes
2answers
1k views

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....
2
votes
1answer
277 views

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 ...
11
votes
3answers
1k views

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 ...
3
votes
1answer
263 views

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, ...
2
votes
1answer
269 views

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 ...
4
votes
2answers
212 views

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 ...
2
votes
1answer
87 views

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 ...
5
votes
3answers
234 views

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 ...
8
votes
1answer
178 views

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 ...
1
vote
2answers
217 views

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 $[...
1
vote
2answers
110 views

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 ...
5
votes
4answers
588 views

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 ...
4
votes
1answer
200 views

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}{...
4
votes
1answer
185 views

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 ...
11
votes
2answers
803 views

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 ...
3
votes
0answers
185 views

Even and primes puzzle?

this is secret numbers that increase regularly, what is the order? If you like numbers, it will be fun. $2^3 \times224299$ $2^2 \times 3^2 \times 19 \times 3557$ $2 \times 5 \times 320647$ $2 \times ...
2
votes
1answer
171 views

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 ...
6
votes
3answers
346 views

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 ...
1
vote
1answer
145 views

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 ...
13
votes
1answer
403 views

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 ...
6
votes
2answers
407 views

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 ...
3
votes
1answer
148 views

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 ...
4
votes
1answer
205 views

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 ...
7
votes
2answers
1k views

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 ...
6
votes
1answer
357 views

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 ...
10
votes
6answers
616 views

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 ...
12
votes
2answers
2k views

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 ...
16
votes
3answers
1k views

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 ...
18
votes
1answer
465 views

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 ...
47
votes
5answers
4k views

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 ...
7
votes
1answer
532 views

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 ...
13
votes
4answers
1k views

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 ...
13
votes
1answer
335 views

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 ...
16
votes
3answers
3k views

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. + ...
4
votes
1answer
237 views

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 ...
2
votes
1answer
118 views

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?
5
votes
2answers
308 views

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 ...
15
votes
5answers
988 views

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 $...
16
votes
1answer
1k views

Prime tree game

Let's play a game. On the first step you place the number 1. On the $n$-th step starting from $n=2$ you place the number $n$ such that: It is adjacent (horizontally or vertically) to one or more ...
4
votes
1answer
173 views

Prime magic star

Can you replace the letters with 10 consecutive primes such that the sum of numbers on each line is equal? I expect this to be solved with a computer. Good luck!
4
votes
2answers
244 views

Primes from arithmetic and geometric progressions

The five primes, 131, 157, 211, 349, 739, are neither in arithmetic or geometric progression, but are instead the sum of the corresponding terms of two progressions of five terms each, one arithmetic ...
1
vote
1answer
126 views

Neighbouring numbers summing to a prime on a 4x4

Can you place every number from 1 to 16 on a 4x4 grid such that every pair of neighbouring (horizontally and vertically) numbers sum to a prime? Note that the generated primes can be reused. A ...
4
votes
3answers
554 views

Neighbouring numbers summing to a prime on a 3x3

Can you place distinct numbers from 0 to 9 on a 3x3 grid such that every pair of neighbouring (horizontally and vertically) numbers sum to a prime? Can you find multiple solutions? Note that the ...
6
votes
4answers
2k views

Smallest number containing the first 11 primes as sub-strings

113257 contains the first 6 primes as sub-strings when reading them from left to right: 2: 113257 3: 113257 5: 113257 7: 113257 11: 113257 13: 113257 What is the smallest number that contains ...
6
votes
2answers
567 views

The largest Thursday number

A Thursday number is a number 𝑁 where any three consecutive digits make a prime, and all such primes formed are distinct. For example, 13739 is a Thursday number because 137, 373, and 739 are all ...