Hello,

Basically I have to construct a sequence that maximises the number of times such that given any pair of numbers, the left-hand one will be greater than the right-hand one. The sum of the positive integer sequence must be 2014.

An example is 7,4,1,3,2

We can select (7,4) ; (7,1) ; (7,3) ; (7,2) ; (4,1) ; (4,3) ; (4,2) ; (3,2) such that the number occurring first is greater than the number occurring last (i.e. LH number > RH number)

So far I figure it will be {2,2......,2,2} (504 2s) and then {1,1,.....,1,1} (1006 1s). \

The two reasons for this are that we should keep a maximum difference at one between numbers otherwise we are unnecessarily adding numbers. The second is that the use of only 2s and 1s will assist in keeping the sum small.

Is this correct and is there a formal way of writing what I have said if it is correct?

Thank you