OME 1994 Problem 3

A tourist office was investigating the numbers of sunny and rainy days in a year in each of six regions. The results are partly shown in the following table:

Region , sunny or rainy , unclassified $A \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, 336 \,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\, 29$ $B \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, 321 \,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\, 44$ $C \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, 335 \,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\, 30$ $D \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, 343 \,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\, 22$ $E \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, 329 \,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\, 36$ $F \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, 330 \,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\, 35$ Looking at the detailed data, an officer observed that if one region is excluded, then the total number of rainy days in the other regions equals one third of the total number of sunny days in these regions. Determine which region is excluded.