A word problem in elementary mathematics is a mathematical exercise stated in ordinary language, often describing a practical situation. Solving it requires interpreting
the stated relationships and expressing them as an arithmetic
calculation or an equation (Marecek et al. 2020,
§3.1). For example, "A box contains 12 pencils and 5 are removed. How many
remain?" is a word problem whose solution is given by the subtraction 
, so 7 pencils remain.
The same term has a technical use in group theory. The group word problem for a finitely generated group asks for an algorithm to decide whether a finite word in group generators and their inverses represents the identity element (Dison et al. 2018). Here a word is a sequence of group generators and their inverses, rather than a statement in ordinary language.
