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.