text: It's very easy to answer this question. We can find the no. of times all the 5 groups met on one and the same day in the first quarter- the New Year's Day excluded- by finding the least common multiple of 2, 3, 4, 5 and 6. This isn't difficult. It's 60.\nTherefore, the 5 will all meet again on the 61st day.\nAll the 5 groups can meet on the one and same day only once in 60 days. And since there are 90 days in the 1st quarter, it means there can only be one other day on which they all meet.\nNow, coming to the 2nd question, this is positively more difficult to find the answer.\nTo find the answer to this, it is necessary to write down all the no.s from 1 to 90 and then strike out all the days when the Literary Group meets- for eg., the 1st, 3rd, 5th, 7th, 9th etc.\nThen we must cross out the Dramatic Group days- for eg., 4th, 7th, 10th etc.\nThis way, we must cross out the days of the Musical, Dancing and Painting Groups also. Then,the no.s that remain are the days when none of the groups meet.\nWhen we do that, we will find that there are 24 such days- 8 in January (2, 8, 12, 14, 18, 20, 24 and 30), 7 in February and nine in March.!!!