Multiple Labeled Tables

Some problems require three dimensional tables just to organize their own data. These problems are characterized by giving two sets of facts such that each set requires its own table. A solution is obtained by relating the two tables with an equation. In these problems, the row labels are the same for the two tables so a diagram sketch is not required. However, since these problems have two tables with the same row and column names, the tables are labeled with different names in the upper left hand corners. As an example of this type of problem consider:

Ann is fifteen years older than Joe. Ten years from now, Ann will be twice as old as Joe. How old is each now?

One table is set up for the current or "now" age relationship and one table is set up for the second or "then" relationship. The two tables are:

                                                  
           ---------------------------------    ---------------------------------
           |now |unknown |factor |term |age|    |then|unknown |factor |term |age|
           ---------------------------------    ---------------------------------                         
           |Ann |        |   1   | 15  |   |    |Ann |        |   2   | 15  |   |
           ---------------------------------    ---------------------------------                         
           |Joe |        |   1   |  0  |   |    |Joe |        |   1   |  0  |   |
           ---------------------------------    ---------------------------------

The possessive form of the table names can be used to identify specific values. For example, the cell corresponding to "ann's factor" is ambiguous since it applies to cells in both tables. However, "Ann's now's factor" and "Ann's then's factor" are unique (The alternative notation "Ann's now factor" and "Ann's then factor" is also acceptable.)

The name of the table can also be used to restricted plurals. For example,

          for ann and joe:

would have the scope of all "ann"s and "joe"s in all tables. While

          for now's ann and joe:

restricts the scope to the now table. The table names may be used alone to refer to entire tables. Multiple tables and entries may be specified in the for statements.

Examples:
          for now:
          for now and then:
          for now, then and ago:
          for now's and then's ann$ and joe$:
          for now's, then's and ago's ann$, bill$ and joe$: