Without assuming any solar models and neutrino flavor conversions, $^8$B neutrinos seen by the Kamiokande experiment should contribute 2.6$\pm 0.45$ SNU to the chlorine experiment. When this rate is compared with the total event rate of 2.3$\pm 0.2$ SNU observed by the Homestake experiment which should inlude a 0.2 SNU contribution from uncertainty-free pep neutrinos, there may still be a possible evidence that $^7$Be neutrinos are more severely suppressed than the $^8$B neutrinos with respect to the predictions of standard solar models, which cannot be explained by any known astrophysics solution. Given a Kamiokande event rate of larger than 36$\%$ (2$��$) of the prediciton of Bahcall and Pinsonneault's standard solar model, variations of standard solar models yield minimal rates of 3.6 SNU for the Homestake experiment and 114 SNU for GALLEX and SAGE. Therefore, variations of standard solar models as solutions to the solar neutrino problem are so far inconsistent with the Homestake experiment and only marginally allowed by the gallium experiments. If the gallium experiments confirm a flux significantly below 114 SNU, it would imply unconventional physics.

revtex 17 pages, 3 figures upon request