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34 votes
Accepted

Prime Number Snake

First, we want to take a look at the snake itself. Then, let's take a look at the grid, and see if there are some obvious features. So, let's fill those in: Then, because the snake has more white ...
Bass's user avatar
  • 77.6k
21 votes
Accepted

Prime tree game

The answer is PROBABLY I don't have a proof yet, but experimenting with it will yield something like My strategy is Now my reasoning is that One idea to rigorously prove it is to use some result ...
WhatsUp's user avatar
  • 7,397
19 votes
Accepted

Prime to Prime: Get all first 25 Prime Numbers using up to 4 Primes

Using 2,3,7,11: $2 = 2$ $3 = 3$ $5 = 11 + 3 - 7 -2$ $7 = 7$ $11 = 11$ $13 = 2 + 11$ $17 = 3! + 11$ $19 = 2^3 + 11$ $23 = 3 \cdot 7 + 2$ $29 = \frac{(7-2)!}{3} - 11$ $31 = 3 \cdot 11- 2$ $37 = (11-3!) ...
ThomasL's user avatar
  • 12.2k
18 votes
Accepted

It's my sister's birthday

Solution Your sister is and the age on the cake is Proof of uniqueness We're given several pieces of information: "transposed the digits of her age" - her age is 2 digits. "She'll thank you for ...
Rand al'Thor's user avatar
15 votes
Accepted

Dividing the first 20 numbers into 3 lists

It is possible to solve this without a computer search. The proof of $\min|O|$ is below.
TheSimpliFire's user avatar
15 votes
Accepted

Gaby's Puzzle (Primes Around a Circle)

The full list of possibilities that each prime can be adjacent to is as follows: The key ones to notice are Now there are only two possibilities for the other number next to $5$, namely $11$ or $41$....
Rand al'Thor's user avatar
15 votes

My library membership number

The number Explanation: Now
Gareth McCaughan's user avatar
14 votes
Accepted

A Prime Number equation using all nine digits once

My answer (worked by hand):
Weather Vane's user avatar
  • 14.5k
14 votes
Accepted

Relatively prime numbers

tehtmi's user avatar
  • 3,316
13 votes
Accepted

Smallest number containing the first 11 primes as sub-strings

Given the first 11 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 We can observe that: We'll always get 2, 3 and 7 for "free" (via other numbers, such as 23 and 17, etc), so they can be ignored ...
Alconja's user avatar
  • 37.3k
13 votes

Scrabble with prime numbers!

This is a huge question, and I think people can help each other here so I'm going to start with some initial strategy: I have set up this board: Which allows for this move: For a score of 2372 (...
TwoBitOperation's user avatar
12 votes

A King's Hamiltonian Tours

One solution to part A:
mbingo's user avatar
  • 1,231
12 votes
Accepted

8x8 square with no adjacent numbers summing to a prime

I think this works: The adjacent number pairs are restricted to where each pair sums to Note that it is necessary to because
Bubbler's user avatar
  • 14.7k
11 votes
Accepted

Prime to Prime Sequel

Here is the answer: $2=2$ $3=3$ $5=2+3$ $7=\frac{43-3}{2}-13$ $11=43-2\cdot(13+3)$ $13=13$ $17=43-13\cdot2$ $19=13+3\cdot2$ $23=43-2\cdot(13-3)$ $29=43-...
Oray's user avatar
  • 30.3k
11 votes
Accepted

Prime number snake (2)

(The earlier version of this answer contained more praise for this puzzle, sometimes comparing it to the earlier one. I only now noticed that this snake was indeed not posted by the OP of the original ...
Bass's user avatar
  • 77.6k
11 votes

Villeta's Soup of Primes

i) ii)
Manish Kundu's user avatar
  • 2,684
11 votes

A Prime Number equation using all nine digits once

Manish Kundu's user avatar
  • 2,684
10 votes
Accepted

Living in prime years

They were born in the year In fact, note that
ZanyG's user avatar
  • 2,595
10 votes
Accepted

Reconstructing the results of a 6-team soccer tournament

First: Now: Next: Now We're nearly there. Let's draw up a table. Entries are scores for the team on the left when they played against the team on the top. And So we're done, and here is the ...
Gareth McCaughan's user avatar
10 votes

A King's Hamiltonian Tours

Solution for the $5$x$5$ grid Other solutions for the same grid are For the $6$x$6$ grid I noted that This leads to this conclusion for the $6$x$6$ grid
spyr03's user avatar
  • 241
10 votes
Accepted

Prime to number conversion

It might be more fun to fill the whole table. I've started with a few examples: $$\require{begingroup}\begingroup \def\*{\times } \begin{array}{|c|c|c|c|c|} \hline n& 2,3,5 & 2,3,7 ...
10 votes
Accepted

Scrabble with prime numbers!

EDIT2: My solution was already accepted, but (I assumed) far from optimal. I finally made myself a prime checking algorithm and checked the 32 numbers that allow maximum scoring for the main 'word'. ...
Retudin's user avatar
  • 9,218
10 votes

A Prime Ant's Excursion in the Cartesian Plane

melmackian's user avatar
9 votes

Prime to Prime: Get all first 25 Prime Numbers using up to 4 Primes

83 is probably not allowed - I swear I'll find a legitimate solution soon... arrgh... Using 2,3,5,7: $2, 3, 5, 7 = 2, 3, 5, 7$ $11 = 7 + 5 + 2 - 3$ $13 = 7 + 5 + 3 - 2$ $17 = 7 \cdot 2 + 3$ $19 = 7 \...
Quintec's user avatar
  • 6,778
9 votes

Dividing the first 20 numbers into 3 lists

Incorrect answer Oops! The "solution" below is wrong in the following way: Unfortunately it's 3:25am local time and I don't have time to attempt a proper fix. My apologies; hopefully someone else ...
Gareth McCaughan's user avatar
9 votes

Find an integer where each sum of 5 consecutive digits is prime

Improving upon Gareth's answer (the details of which I will not repeat) with consideration of ThomasL's suggestion, a solution with 12 primes is found: Two solutions with 11 primes were also found:
Daniel Mathias's user avatar
9 votes
Accepted

Splitting the Primes

Parcly Taxel's user avatar
  • 7,720
8 votes
Accepted

Two equal-sized lists that produce prime sums

Computer search solution. A quick and dirty Python script then identifies... Here is the script: ...
Uri Granta's user avatar
  • 1,134
8 votes

A King's Hamiltonian Tours

A solution for part B:
Glorfindel's user avatar
  • 28.1k
8 votes

It's my sister's birthday

She was The decorator put
SteveV's user avatar
  • 15.9k

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