During a school year Andrew was given 40 mathematical problems as part of his assessment, one problem per week. As a result of marking he could receive 2,3,4 or 5 marks for each problem. Andrew called his result for any problem "unexpected" if up to that week the same mark occurred a lesser number of times than any other mark. For example, if for the first 10 problems, in order Andrew's marks were 3,4, ....,3, then his "unexpected" marks would have been 5 when it occurred for the first time, and 4 when it occurred for the second time. At the end of the year Andrew received 10 results of 2 marks each, 10 results of 3 marks each, 10 results of 4 marks each and 10 results of 5 marks each, though it not known in which order. Is it possible to determine for sure how many results were "unexpected" for Andrew?
I am still slightly unclear about what unexpected is and am not sure how I would prove whether or not it is possible to find the number of "unexpected" results for Andrew. I would really appreciate easy-to understand explanations. Thank you.