First-year math students were asked whether they experience math anxiety, headaches, or tiredness when studying for math exams. Of the 125 students asked, 66 experience math anxiety, 22 experience headaches, 51 experience tiredness, 10 get headaches and math anxiety, 22 get tired and experience math anxiety, 11 experience tiredness and headaches, and 17 fortunate students said they experience none of the three problems. How many of the students surveyed experience all three problems?
This is a basic PIE question i get 12 which is impossible.
$A=66 \space$, $H=22\space$, $T=51\space $, $H\cap A = 10\space$, $T \cap A= 22 \space, T\cap H = 11$
$A\cup H\cup T = 125-17=108 $
$$A\cup H\cup T = A +H +T - H\cap A -T \cap A \space - T\cap H + A\cap H \cap T$$
$$108=139-10-22-11+A\cap H \cap T$$
$$A\cap H \cap T = 12$$ Which is impossible as it is at most 10.
As has been discussed in the comments, the problem is indeed infeasible; your calculations are correct.