MATH OLYMPIAD (1998) Session I Problem
SCORING GUIDE (RUBRIC)

SCORE

DESCRIPTION

4
  • All building code limits are met
  • All drawings are complete and accurate with dimensions.
  • The floor plan is square.
  • Design quality is computed accurately.
  • They stayed within the 100 board limit.
  • The quality measure "Q" is equal to or greater than 30.
  • Design shows some innovation. (see nuggets list)

 

3
  • All building code limits are adhered to.
  • The drawings are done, but are a little sloppy. Not all dimensions are included.
  • They stayed within the 100 board limit
  • The quality measure "Q" is computed accurately.

 

2
  • A significant response to the problem that falls below a 3. Building code limits are violated, but all asked for response elements are present.

1
  • All other responses

 

LIST OF "NUGGETS"

Things to look for in a team response:

  1. Square interior floor plan is optimal.
  2. Board thickness is considered in wall width calculations (Figures 1-A and 1-B).
  3. Equal wall widths are best (Figure 1-A).
  4. Wall width is integral multiple of stud spacing. (This is actually a requirement)
  5. Window widths are integral multiples of stud spacing. (This is actually a requirement)
  6. More than one window per wall is used.
  7. The window width is N S - 2 inches, where S is the space between studs, and N is the number of studs. For example, if there are 24 inches between studs, and the window is 3 studs wide, the window width = 3 x 24 - 2 = 70 inches. (2 in the formula takes stud thickness into consideration.)

 

SCORING CONSIDERATIONS

The requirement that all studs be spaced equally means that the best design will have 4 equal-width walls. The only way to get this with a square floor plan looks something like this.
Figure 1A:

This fact is left as something for a top scoring team to discover.

 

Here is an inferior solution:
Figure 1B:

 

Here are poor solutions. They do not consider stud width. The rightmost one has an outer shape that is NOT rectangular.