A box contains 500 marbles with 5 different colours. Which each colour marbles amounted 100. Minimum number of marbles that must be taken randomly, so the drawn marbles are guaranteed to load at least 5 marbles of the same colours is ...

Question

anonymous · Answer

By the pigeonhole principle it must be $5\cdot 4+1$. The worst possible scenario is picking different marbles, this can only happen a maximum of 5 times, as the sixth there must be a repetition. Continuing this case four more times, then we have the above.

kaederfds · Answer

so the answer is 21?