Your teacher has a total of 25 chalk sticks. When a chalk stick reduces to 1/5 of its original size, it gets too small for her to hold for writing and so she puts it to one side. But your teacher hates wasting things and so, when she knows that she has enough of these small pieces to join together to make another chalk stick of the same size, she joins them and uses the new chalk stick. If she uses one chalk stick each day, how many days will the 25 chalk sticks last?

There is a common English word that is nine letters long. Each time you remove a letter from it, it still remains an English word - from nine letters right down to a single letter. What is the original word, and what are the words that it becomes after removing one letter at a time? (The letters can be removed from anywhere in the word - not just the beginning or end).