Apart from the separating words problem (see other answer to this question) and the problem on Peirce expansion (still another answer), Jeffrey Shallit offered cash prizes, ranging from £10 to £200, for 17 further problems in the following talk.

Jeffrey Shallit. Open problems in automata theory: an idiosyncratic view, LMS Keynote Address in Discrete Mathematics, BCTCS 2014, April 10 2014, Loughborough, England

As stated on his "talks" page, Problem 10 on slide 37 has been solved, and the prize was rewarded at WORDS 2015.

Apart from the separating words problem (see other answer to this question) and the problem on Pierce expansion (still another answer), Jeffrey Shallit offered cash prizes, ranging from £10 to £200, for 17 further problems in the following talk.

Jeffrey Shallit. Open problems in automata theory: an idiosyncratic view, LMS Keynote Address in Discrete Mathematics, BCTCS 2014, April 10 2014, Loughborough, England

As stated on his "talks" page, Problem 10 on slide 37 has been solved, and the prize was rewarded at WORDS 2015.