I am going to a particularly reasonable college that likes to ensure that each scholar will get their greatest shot. One manner they guarantee that is by their rounding system. The guidelines are as follows:

• All marks for all items of labor are out of 100
• Any marks which might be inside 1.5 of a a number of of ten may be rounded as much as the closest a number of of ten.
• Sets of marks may be averaged to provide a brand new mark. These new common marks can then be rounded up and averaged with different marks.
• In the top the scholar will get a single mark which is shaped by the repeated averaging and rounding up course of.

Using this technique it’s attainable that the ultimate mark awarded is numerous bigger than the common of all of the marks.

For instance, if a scholar solely will get one mark and it’s 68.5, this may be rounded as much as 70. This is 1.5 bigger than the conventional common (of just one mark).

If a scholar get two marks that are 38.5 and 77, then the 38.5 may be rounded as much as 40 after which the 40 and 77 may be averaged to provide 58.5 which may in flip by rounded as much as 60. The common of 38.5 and 77 would have been 57.75 so 60 is 2.25 bigger than this common.

This query is that this: for every variety of items of labor, what’s the largest hole that one can obtain between the conventional common and this repeated rounding up common?