A penny collection contains twelve 1976 pennies, seven 1968 pennies and eleven 1971 pennies. If you are to pick some pennies without looking at the dates, what is the least number that you must pick to be sure of getting at least five pennies from the same year?
I tried the generalized principle: N(X)>k.N(Y) where N(X) defines the number of pennies. So it should be 30>6.5 --> But the solution says 13. Am i applying the principle wrongly?
Just think about it intuitively. The worst case scenario is that you have already selected 4 pennies of each date. There are 3 dates, giving you 12 pennies selected. The next one you pick guarantees that you will have at least 5 pennies for at least one date. Thus, taking 13 pennies guarantees you will have at least 5 of at least one date.