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31 votes
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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 ...
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21 votes
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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 ...
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  • 6,402
19 votes
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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!) ...
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18 votes
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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 ...
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15 votes
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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.
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15 votes
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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 $41$....
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13 votes
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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 ...
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12 votes

A King's Hamiltonian Tours

One solution to part A:
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  • 1,231
12 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 (...
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11 votes
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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 ...
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11 votes
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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 ...
11 votes
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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
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10 votes
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Living in prime years

They were born in the year In fact, note that
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  • 2,545
10 votes
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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 ...
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10 votes
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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-...
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  • 28.8k
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
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  • 241
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 \...
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  • 6,750
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 ...
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9 votes

Prime to number conversion

I tried writing a generator. I can get everything from 1 to 24 inclusive, for all 4 combinations. I can get 0 to 33 for one combination. The first ungeneratable counting number is 68. $$\begin{...
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  • 1,532
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:
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9 votes
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Splitting the Primes

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9 votes
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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'. ...
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  • 4,767
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: ...
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  • 1,124
8 votes

A King's Hamiltonian Tours

A solution for part B:
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8 votes

It's my sister's birthday

She was The decorator put
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  • 14.8k
8 votes
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Find an integer where each sum of 5 consecutive digits is prime

New high score :P List of possible primes is 43, 41, 37, 31, 29, 23, 19, 17, 13, 11, 7, 5, 3, 2. Distances between those primes are 2, 4, 6, 2, 6, 4, 2, 4, 2, 4, 2, 2, 1. Which? The key observation:...
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  • 1,545
8 votes

Splitting the Primes

A quick calculation first Parity argument Slightly more detail Answer
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  • 122k
8 votes
Accepted

A prime time traveler

There are 25 primes below 100: 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 So the question is whether we can gather 24 variants plus yourself in one ...
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7 votes

Prime Number Snake

Partial answer, to be used as a springboard Parity The first thing to notice is that Then, of course, We notice also that Prime gaps The primes between 1 and 100 are: ...
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7 votes
Accepted

Can you cut through the mist?

I think the answer is Reasoning Example
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