Did you solve it? Gödel’s incompleteness theorem

The solution to today's puzzle

Earlier today I set you the puzzle below, which is based on Godel's incompleteness theorem. As I discussed in the original post, this theorem is one of the most famous in maths and states that in any mathematical system there will always be true statements that cannot be proved.

For example, in a formal mathematical setting, the statement This sentence is unprovable" is both true and formally unprovable. When Godel published his theorem in 1931 it up-ended the study of the foundations of mathematics and its consequences are still being felt today.