Is $L = \{ a^ib^j : 0 < j < i < 2j\}$ context free? How can it be shown?
What's the smallest possible j, and which i goes with it (to allow j &lt; i &lt; 2j). So that's the minimum number of a's and b'. Beyond that, you need one or two a's for every additional b.
That should be enough to find a grammar.