Questions tagged [primes]

A puzzle that involves and requires knowledge of prime numbers.

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11
votes
1answer
291 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
381 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
90 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
139 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
631 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
296 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
609 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 ...
14
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
391 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 ...
46
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
435 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
312 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
233 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
111 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
294 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
976 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 $...
14
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
162 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
237 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
102 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
515 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 ...
7
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 ...