user295: Being able to search for question which have not attached much answers would be helpful for a Q & A site. Currently unanswered only shows question with no answered that has received an upvotes. This is a bit limiting as there might be questions which can get better answers but not necessarily without upvotes.
So it would be good to have a way to search questions fitting a much broader search criteria.

user7: You can do this straight from the Buddhism SE search box.

To search for only questions that fall within a particular range for score, number of answers, or number of views, you can enter an upper or lower parameter, or a range.

score:-1 or score:-1.. will both return posts with a score greater than or equal to -1
views:500..1000 or views:500-1000 will return posts with 500 to 1000 views
answers:..3 will return questions with 3 or fewer answers


More tips on searching are here.
So to find positively scored questions with no answers, try: answers:0 score:1 in the main site search box.

user254: That level of control/customization in not built-in to the site's default user interface.
But, the StackExchange Data Explorer ("SEDE") lets users create and run arbitrary queries.
SEDE queries run against an archived copy of the site data. The archive is generated / backed up each week-end (so a SEDE query won't detect the most recent i.e. this week's questions).
An example of a custom query is Find interesting unanswered questions.
To use this query, enter your own user ID, which I think is 295.
You can edit this query if it doesn't do exactly what you want. For example, this line ...
where (select count(*) from Posts a where a.ParentId = q.Id and a.Score > 0) = 0

... filters/removes (from the list of 'unanswered' results) all topics which have an answer which have a score of greater than 0. The two 0 in the above line correspond to the m and n in your question title: you can edit the query to replace these 0 with other numbers, e.g. 1 and 2.
For example the following looks for topics which have less than two answers that have a score of more than 1:
where (select count(*) from Posts a where a.ParentId = q.Id and a.Score > 1) < 2

This particular query tries to present/filter questions whose tags match the tags which you have historically been able to answer. If you want to remove that filter (so that you see questions regardless of their tags), I suspect it's sufficient to edit/remove this line from the query:
join #tags t on t.TagId = pt.TagId


295: <p>Being able to search for question which have not attached much answers would be helpful for a Q &amp; A site. Currently <code>unanswered</code> only shows question with no answered that has received an upvotes. This is a bit limiting as there might be questions which can get better answers but not necessarily without upvotes.</p>

<p>So it would be good to have a way to search questions fitting a much broader search criteria.</p>
 7: <p>You can do this straight from the Buddhism SE search box.</p>
<blockquote>
<p>To search for only questions that fall within a particular range for score, number of answers, or number of views, you can enter an upper or lower parameter, or a range.</p>
<ul>
<li><code>score:-1</code> or <code>score:-1..</code> will both return posts with a score greater than or equal to -1</li>
<li><code>views:500..1000</code> or <code>views:500-1000</code> will return posts with 500 to 1000 views</li>
<li><code>answers:..3</code> will return questions with 3 or fewer answers</li>
</ul>
</blockquote>
<p><a href="https://buddhism.stackexchange.com/help/searching">More tips on searching are here.</a></p>
<p>So to find positively scored questions with no answers, try: <code>answers:0 score:1</code> in the main site search box.</p>
 254: <p>That level of control/customization in not built-in to the site's default user interface.</p>

<p>But, the StackExchange Data Explorer ("SEDE") lets users create and run arbitrary queries.</p>

<p>SEDE queries run against an archived copy of the site data. The archive is generated / backed up each week-end (so a SEDE query won't detect the most recent i.e. this week's questions).</p>

<p>An example of a custom query is <a href="http://data.stackexchange.com/buddhism/query/4038/find-interesting-unanswered-questions" rel="nofollow noreferrer">Find interesting unanswered questions</a>.</p>

<p>To use this query, enter your own user ID, which I think is <a href="https://buddhism.meta.stackexchange.com/users/295/suminda-sirinath-salpitikorala">295</a>.</p>

<p>You can edit this query if it doesn't do exactly what you want. For example, this line ...</p>

<pre><code>where (select count(*) from Posts a where a.ParentId = q.Id and a.Score &gt; 0) = 0
</code></pre>

<p>... filters/removes (from the list of 'unanswered' results) all topics which have an answer which have a score of greater than 0. The two <code>0</code> in the above line correspond to the <code>m</code> and <code>n</code> in your question title: you can edit the query to replace these <code>0</code> with other numbers, e.g. <code>1</code> and <code>2</code>.</p>

<p>For example the following looks for topics which have less than two answers that have a score of more than 1:</p>

<pre><code>where (select count(*) from Posts a where a.ParentId = q.Id and a.Score &gt; 1) &lt; 2
</code></pre>

<p>This particular query tries to present/filter questions whose tags match the tags which you have historically been able to answer. If you want to remove that filter (so that you see questions regardless of their tags), I suspect it's sufficient to edit/remove this line from the query:</p>

<pre><code>join #tags t on t.TagId = pt.TagId
</code></pre>
