Three Exercises
1. Three people picked a number of apples and divided them according to their ages. Sione took three more apples than Petra, while David took twice as many as Sione, which gave him eleven more than Petra.
How many apples were there in total ?
2. Convince yourself that adding a sequence of consecutive odd numbers starting from 1 will always result in a number which is a perfect square.
3. Explore what happens if you start with any number, square each digit, add the result, then do the same again, and so on.