in the first case, ie {{Problem | hint}}, the first argument is considered to be a nameless argument, and can be tested as <if 1></if> and used as {{{1}}}.

In the case of the problem template, one way to do it like the first case might be to use:

• [/attempts]
• [/solution]
• <if 1>[/{{{1}}}]</if>
• <if 2>[/{{{1}}}]</if>

which would allow {{problem|hint|discussion}} to work.