Save your pickaxes. I transmuted 1000 so I could use them all; digging out floor 80. It is 30x30 tiles filled only with my regret for the wasted magic pickaxes.
Quick Tips because this is a headache of a medium badge - Spoilers - You are not required to solve any puzzles. If you are stuck you can simply give up. If you do not see the give up option, reload. This goes for the tea puzzle, chemistry puzzle, dream puzzles etc. If you are stuck on the algebra puzzle at the start I believe the answer is 9. When you have to talk to mother superior make sure you exhaust dialogue options with everyone and then simply draw three matches from your book (icon in top right) before speaking with her. The matches usually have the same numbers in the descriptions.