31
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 ...
- 76k
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 ...
- 7,357
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!) ...
- 11.9k
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 ...
- 116k
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.
- 3,604
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 $41$....
- 116k
15
votes
14
votes
Accepted
14
votes
Accepted
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 ...
- 37.1k
13
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
- 11.6k
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 (...
- 15k
12
votes
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 ...
- 76k
11
votes
11
votes
10
votes
Accepted
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 ...
- 117k
10
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-...
- 30.2k
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
- 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'.
...
- 8,010
10
votes
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 \...
- 6,768
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 ...
- 117k
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:
- 13.4k
9
votes
Accepted
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:
...
- 1,134
8
votes
8
votes
Only top scored, non community-wiki answers of a minimum length are eligible