Happy Valentine's Day, once againNumber Theory Level 5
Comrade Vladimir is getting some flowers for Nadezhda, his Valentine. Being of a precise analytical mind, he plans to spend exactly 100 rubles on exactly 100 flowers. At the flower market, they sell daisies at a rate of 5 for 3 rubles, tulips at a rate of 7 for 5 rubles, carnations at a rate of 9 for 7 rubles, and roses at a rate of 3 for 9 rubles.
To qualify for these special rates, one needs to buy daisies in bunches of 5, tulips in bunches of 7, etc. In how many different ways can Vladimir select a bunch of 100 flowers that will contain some flowers of all four kinds while still qualifying for these special rates?