The word "solvable" means that a problem or puzzle has a solution that can be found or figured out. Full definition
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: Finding Solutions and Managing Dilemmas (Teachers College Press, 2001) that such value conflicts present not solvable problems, but a dilemma that needs ongoing management. (educationworld.com)
Poverty and social exclusion - the EU's theme for 2010 - are «structural problems not solvable by charity or by sticking - plaster handouts of welfare payments, however necessary they may be in the short term». (politics.co.uk)
17 In his teens, Evariste Galois invented an entirely new branch of math, called group theory, to prove that «the quintic» — an equation with a term of x5 — was not solvable by any formula. (discovermagazine.com)