Is there an easier (or alternative) method to uncover the answer, as opposed to brute-force/exhaustion?
Clash Royale CLAN TAG#URR8PPP
up vote
2
down vote
favorite
Here is a puzzle I made (I originally posted it here on the Puzzling Stack Exchange):
Suppose you constructed $m$ rows in the following way ($m,n$ are integers): $$beginalign&1,2,3,ldots ,n \ &n+1,ldots , 2n \ &2n+1,ldots 3nendalign$$ $$vdots$$ $$n(m-1)+1,ldots, mn$$ In each row, you want to have an odd number of odd primes. If $m<13$, what prime number $n$ can you find that will form the highest possible prime value of $m$?
The answer is hidden in the puzzle...
I created such a puzzle because a user wanted to find puzzles that had the answer hidden in the puzzle itself. I will not tell you what the answer is; I only posted this as a question because I do have a question:
Question:
Suppose you did not know the answer, or at least did not know that the answer was hidden in the puzzle. Is there a way to find out the answer without brute-force/exhaustion? Otherwise the puzzle may seem a bit boring or tiring, which I don't want to make other users feel.
Also, there might be multiple values of $n$, so I fear this puzzle might be too broad, so I will just say now, the proposed solution is between $1$ and $20$ (inclusive, just to increase the potential possibilities at first glance!).
Apologies if this question is not appropriate for the site, as it is not a "typical" question like others. Also, I was not fully sure what tags were appropriate either, so sorry if they are not.
Thank you in advance.
Edit:
I now feel a little more relaxed about whether or not this is an appropriate question, after checking out this post.
proof-writing prime-numbers puzzle
asked Aug 24 at 0:08
user477343
4,26231139
 |Â
show 5 more comments
up vote
2
down vote
favorite
Here is a puzzle I made (I originally posted it here on the Puzzling Stack Exchange):
Suppose you constructed $m$ rows in the following way ($m,n$ are integers): $$beginalign&1,2,3,ldots ,n \ &n+1,ldots , 2n \ &2n+1,ldots 3nendalign$$ $$vdots$$ $$n(m-1)+1,ldots, mn$$ In each row, you want to have an odd number of odd primes. If $m<13$, what prime number $n$ can you find that will form the highest possible prime value of $m$?
The answer is hidden in the puzzle...
I created such a puzzle because a user wanted to find puzzles that had the answer hidden in the puzzle itself. I will not tell you what the answer is; I only posted this as a question because I do have a question:
Question:
Suppose you did not know the answer, or at least did not know that the answer was hidden in the puzzle. Is there a way to find out the answer without brute-force/exhaustion? Otherwise the puzzle may seem a bit boring or tiring, which I don't want to make other users feel.
Also, there might be multiple values of $n$, so I fear this puzzle might be too broad, so I will just say now, the proposed solution is between $1$ and $20$ (inclusive, just to increase the potential possibilities at first glance!).
Apologies if this question is not appropriate for the site, as it is not a "typical" question like others. Also, I was not fully sure what tags were appropriate either, so sorry if they are not.
Thank you in advance.
Edit:
I now feel a little more relaxed about whether or not this is an appropriate question, after checking out this post.
proof-writing prime-numbers puzzle
asked Aug 24 at 0:08
user477343
4,26231139
1
While this is an appropriate question, you shouldn't use questions like "What are good math puzzles" as models for your own. They tend to be the exception, not the norm.
– Rushabh Mehta
Aug 24 at 1:04
1
btw since you mention the intended range for $n$, I wonder if your intended solution is $n=13$? Note that $n=13$ only achieves $m=11$, while $n=4843$ achieves $m=12$.
– stewbasic
Aug 24 at 1:08
1
@RushabhMehta Done! :)
– user477343
Aug 24 at 1:17
2
@user477343 I'm not convinced there's a better way than brute. Prime numbers are notoriously annoying
– Rushabh Mehta
Aug 24 at 1:19
1
@user477343 This doesn't fix it; $n=165941$ is prime and achieves $m=12$. Naively I'd expect each integer to have a one in $2^12$ chance of achieving $m=12$. I suggest editing so that $n=13$ reaches the bound you've set (something like "$m+1<13$" but less contrived...)
– stewbasic
Aug 24 at 3:17
 |Â
show 5 more comments
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Here is a puzzle I made (I originally posted it here on the Puzzling Stack Exchange):
Suppose you constructed $m$ rows in the following way ($m,n$ are integers): $$beginalign&1,2,3,ldots ,n \ &n+1,ldots , 2n \ &2n+1,ldots 3nendalign$$ $$vdots$$ $$n(m-1)+1,ldots, mn$$ In each row, you want to have an odd number of odd primes. If $m<13$, what prime number $n$ can you find that will form the highest possible prime value of $m$?
The answer is hidden in the puzzle...
I created such a puzzle because a user wanted to find puzzles that had the answer hidden in the puzzle itself. I will not tell you what the answer is; I only posted this as a question because I do have a question:
Question:
Suppose you did not know the answer, or at least did not know that the answer was hidden in the puzzle. Is there a way to find out the answer without brute-force/exhaustion? Otherwise the puzzle may seem a bit boring or tiring, which I don't want to make other users feel.
Also, there might be multiple values of $n$, so I fear this puzzle might be too broad, so I will just say now, the proposed solution is between $1$ and $20$ (inclusive, just to increase the potential possibilities at first glance!).
Apologies if this question is not appropriate for the site, as it is not a "typical" question like others. Also, I was not fully sure what tags were appropriate either, so sorry if they are not.
Thank you in advance.
Edit:
I now feel a little more relaxed about whether or not this is an appropriate question, after checking out this post.
proof-writing prime-numbers puzzle
asked Aug 24 at 0:08
user477343
4,26231139
Here is a puzzle I made (I originally posted it here on the Puzzling Stack Exchange):
Suppose you constructed $m$ rows in the following way ($m,n$ are integers): $$beginalign&1,2,3,ldots ,n \ &n+1,ldots , 2n \ &2n+1,ldots 3nendalign$$ $$vdots$$ $$n(m-1)+1,ldots, mn$$ In each row, you want to have an odd number of odd primes. If $m<13$, what prime number $n$ can you find that will form the highest possible prime value of $m$?
The answer is hidden in the puzzle...
I created such a puzzle because a user wanted to find puzzles that had the answer hidden in the puzzle itself. I will not tell you what the answer is; I only posted this as a question because I do have a question:
Question:
Suppose you did not know the answer, or at least did not know that the answer was hidden in the puzzle. Is there a way to find out the answer without brute-force/exhaustion? Otherwise the puzzle may seem a bit boring or tiring, which I don't want to make other users feel.
Also, there might be multiple values of $n$, so I fear this puzzle might be too broad, so I will just say now, the proposed solution is between $1$ and $20$ (inclusive, just to increase the potential possibilities at first glance!).
Apologies if this question is not appropriate for the site, as it is not a "typical" question like others. Also, I was not fully sure what tags were appropriate either, so sorry if they are not.
Thank you in advance.
Edit:
I now feel a little more relaxed about whether or not this is an appropriate question, after checking out this post.
proof-writing prime-numbers puzzle
asked Aug 24 at 0:08
user477343
4,26231139
edited Aug 24 at 1:20
asked Aug 24 at 0:08
user477343
4,26231139
asked Aug 24 at 0:08
user477343
4,26231139
asked Aug 24 at 0:08
user477343
4,26231139
4,26231139
1
While this is an appropriate question, you shouldn't use questions like "What are good math puzzles" as models for your own. They tend to be the exception, not the norm.
– Rushabh Mehta
Aug 24 at 1:04
1
btw since you mention the intended range for $n$, I wonder if your intended solution is $n=13$? Note that $n=13$ only achieves $m=11$, while $n=4843$ achieves $m=12$.
– stewbasic
Aug 24 at 1:08
1
@RushabhMehta Done! :)
– user477343
Aug 24 at 1:17
2
@user477343 I'm not convinced there's a better way than brute. Prime numbers are notoriously annoying
– Rushabh Mehta
Aug 24 at 1:19
1
@user477343 This doesn't fix it; $n=165941$ is prime and achieves $m=12$. Naively I'd expect each integer to have a one in $2^12$ chance of achieving $m=12$. I suggest editing so that $n=13$ reaches the bound you've set (something like "$m+1<13$" but less contrived...)
– stewbasic
Aug 24 at 3:17
 |Â
show 5 more comments
1
While this is an appropriate question, you shouldn't use questions like "What are good math puzzles" as models for your own. They tend to be the exception, not the norm.
– Rushabh Mehta
Aug 24 at 1:04
1
btw since you mention the intended range for $n$, I wonder if your intended solution is $n=13$? Note that $n=13$ only achieves $m=11$, while $n=4843$ achieves $m=12$.
– stewbasic
Aug 24 at 1:08
1
@RushabhMehta Done! :)
– user477343
Aug 24 at 1:17
2
@user477343 I'm not convinced there's a better way than brute. Prime numbers are notoriously annoying
– Rushabh Mehta
Aug 24 at 1:19
1
@user477343 This doesn't fix it; $n=165941$ is prime and achieves $m=12$. Naively I'd expect each integer to have a one in $2^12$ chance of achieving $m=12$. I suggest editing so that $n=13$ reaches the bound you've set (something like "$m+1<13$" but less contrived...)
– stewbasic
Aug 24 at 3:17
1
1
While this is an appropriate question, you shouldn't use questions like "What are good math puzzles" as models for your own. They tend to be the exception, not the norm.
– Rushabh Mehta
Aug 24 at 1:04
While this is an appropriate question, you shouldn't use questions like "What are good math puzzles" as models for your own. They tend to be the exception, not the norm.
– Rushabh Mehta
Aug 24 at 1:04
1
1
btw since you mention the intended range for $n$, I wonder if your intended solution is $n=13$? Note that $n=13$ only achieves $m=11$, while $n=4843$ achieves $m=12$.
– stewbasic
Aug 24 at 1:08
btw since you mention the intended range for $n$, I wonder if your intended solution is $n=13$? Note that $n=13$ only achieves $m=11$, while $n=4843$ achieves $m=12$.
– stewbasic
Aug 24 at 1:08
1
1
@RushabhMehta Done! :)
– user477343
Aug 24 at 1:17
@RushabhMehta Done! :)
– user477343
Aug 24 at 1:17
2
2
@user477343 I'm not convinced there's a better way than brute. Prime numbers are notoriously annoying
– Rushabh Mehta
Aug 24 at 1:19
@user477343 I'm not convinced there's a better way than brute. Prime numbers are notoriously annoying
– Rushabh Mehta
Aug 24 at 1:19
1
1
@user477343 This doesn't fix it; $n=165941$ is prime and achieves $m=12$. Naively I'd expect each integer to have a one in $2^12$ chance of achieving $m=12$. I suggest editing so that $n=13$ reaches the bound you've set (something like "$m+1<13$" but less contrived...)
– stewbasic
Aug 24 at 3:17
@user477343 This doesn't fix it; $n=165941$ is prime and achieves $m=12$. Naively I'd expect each integer to have a one in $2^12$ chance of achieving $m=12$. I suggest editing so that $n=13$ reaches the bound you've set (something like "$m+1<13$" but less contrived...)
– stewbasic
Aug 24 at 3:17
 |Â
show 5 more comments
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2892666%2fis-there-an-easier-or-alternative-method-to-uncover-the-answer-as-opposed-to%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
1
While this is an appropriate question, you shouldn't use questions like "What are good math puzzles" as models for your own. They tend to be the exception, not the norm.
– Rushabh Mehta
Aug 24 at 1:04
1
btw since you mention the intended range for $n$, I wonder if your intended solution is $n=13$? Note that $n=13$ only achieves $m=11$, while $n=4843$ achieves $m=12$.
– stewbasic
Aug 24 at 1:08
1
@RushabhMehta Done! :)
– user477343
Aug 24 at 1:17
2
@user477343 I'm not convinced there's a better way than brute. Prime numbers are notoriously annoying
– Rushabh Mehta
Aug 24 at 1:19
1
@user477343 This doesn't fix it; $n=165941$ is prime and achieves $m=12$. Naively I'd expect each integer to have a one in $2^12$ chance of achieving $m=12$. I suggest editing so that $n=13$ reaches the bound you've set (something like "$m+1<13$" but less contrived...)
– stewbasic
Aug 24 at 3:17