Can someone help me on these problems please ?
1. Consider the task of deciding if any given Turing Machine (TM) will from an initial blank tape ever print a non-blank on the initially scanned square. Assuming the Blank Tape Halting Problem (BTHP) Theorem, show that this task is Turing Impossible.
2. Let us call any square on a tape currently significant if it is currently non-blank, or if it is currently scanned, or if it lies between two squares each currently non-blank or scanned, and consider the task of deciding if any given TM from an initially blank tape will ever have more than 100 currently significant squares on its tape. Show that this task is Turing Possible.