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dilemma a problem situation that requires a choice between equally undesirable solutions or that resists satisfactory solution. [1/2 definitions]
do1 to attempt or carry out in order to solve a problem or accomplish a particular goal. [1/13 definitions]
embarrass to complicate (a problem). [1/5 definitions]
episode a physiological event, typically one among others over time, that is a manifestation of an illness or other physical problem. [1/3 definitions]
eureka I have found it! (used to express excitement at having solved a problem or made a discovery).
example a mathematical problem used for illustration. [1/4 definitions]
facet an angle, aspect, or phase, as of a problem or situation. [1/4 definitions]
figure out to find an answer to a problem or puzzling question by using the power of the mind.
glitch (informal) a minor problem, mishap, malfunction, or defect, as in a machine or plan. [1/2 definitions]
Gordian knot a very difficult problem or impasse. [1/2 definitions]
grapple to struggle to master a difficult object, problem, or opponent (often fol. by "with"). [1/6 definitions]
hack1 a creatively improvised or uniquely clever method of solving a problem. [1/12 definitions]
help to cause something to improve, or to bring one closer to a solution to a problem. [2/13 definitions]
hot potato (informal) a problem or issue that is troublesome or esp. difficult to handle.
hydra a many-sided problem that persists or grows worse even after part of it is solved. [1/4 definitions]
insomnia difficulty in getting to sleep, esp. as a persistent problem.
kink a small problem or imperfection that prevents something from working well. [1/5 definitions]
let in mathematics, used to propose that something be accepted as true in order to set up a problem or demonstrate a principle. [1/8 definitions]
look into to investigate or examine (a matter, possible solution, problem, or the like).
make a mountain out of a molehill to imagine something to be much more significant or more of a problem than it really is.
matter problem or trouble (prec. by "the"; often fol. by "with"). [1/8 definitions]