The Australian Mathematics Competition was conducted in Australian schools, two days ago (Thursday 5 Aug). As usual their were some great questions. After the competition was conducted, Mathematics teachers at my school began some very lively, animated discussions. This reminded me about how powerful, group work can be. Here is one question we liked. It is question 29 from the Intermediate (Year 9 & 10) paper:
I have a list of thirty numbers where the first number is 1, the last number is 30, and each of the other numbers is one more than the average of its two neighbours. What is the largest number in the list?
As with many non-routine problems, reading and understanding the problem, is a first vital step. Any comments re this problem?