Students in a class take turns to practise their arithmetic skills. Initially a board contains the integers from 1 to 10 inclusive, each written ten times. On each turn a student first deletes two of the integers and then writes on the board the number that is one more than the sum of those two deleted integers. Turns are taken until there is only one number remaining on the board. Assuming no student makes a mistake, what is the remaining number?
, 2016
Want a route through all this instead of an archive? The track
puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.