A natural number $N$ is less than $$200$$. If $N$ is written in base $$4$$, the sum of the digits is equal to $$5$$. If $N$ is written in base $$6$$, the sum of the digits is equal to $$8$$. If $N$ is written in base $$8$$, the sum of the digits is equal to $$9$$. What is/are the possible value(s) of $N$ it it is written in base $$10$$?  Answer:~\uline{~~~~~~~~~~}~ 
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Binary Linear Equations with Integer Coefficients 