Adding a join and a count to existing query inflates the sums and count function output
select problems.problem_id , problem_title , sum( vote ) as totalVotes
from problems
left join problem_votes on
problems.problem_id = problem_votes.problem_id
left join problem_categories on
problems.problem_id = problem_categories.problem_id
where problem_categories.category_id = 1 GROUP BY problem_title;

select problems.problem_id , problem_title , sum( vote ) as totalVotes , count(solution_name) from problems
left join problem_votes on
problems.problem_id = problem_votes.problem_id
left join problem_categories on
problems.problem_id = problem_categories.problem_id
left join suggested_solutions on
problems.problem_id = suggested_solutions.problem_id
where problem_categories.category_id = 1 GROUP BY problem_title;

SELECT problems.problem_id,
       problem_title,
       SUM(vote) AS totalVotes,
       Solution_Count
FROM   problems
       LEFT JOIN problem_votes
         ON problems.problem_id = problem_votes.problem_id
       LEFT JOIN problem_categories
         ON problems.problem_id = problem_categories.problem_id
       LEFT JOIN (SELECT COUNT(solution_name) AS Solution_Count,
                         problem_id
                  FROM   suggested_solutions
                  GROUP  BY problem_id) ss
         ON problems.problem_id = ss.problem_id
WHERE  problem_categories.category_id = 1
GROUP  BY problem_title;