Read the passage below and solve the questions based on it.
Pankaj has six friends, and during a certain vacation he met them at several dinners. He found that he dined with all six friends exactly one day; with every five of them of 2 days; with every four of them of 3 days; with every three of them of 4 days; with every two of them of 5 days. Further, every friend was present at 8 dinners and every friend was absent at 8 dinners.
How many dinners did Pankaj have alone during the vacation?