13 pennies to be sure of getting at least five pennies from the same year.
To determine the minimum number of pennies you need to pick to be sure of getting at least five pennies from the same year, you can use the Pigeonhole Principle.
The worst-case scenario is that you pick four pennies from each of the years (1967, 1968, and 1971), making a total of 12 pennies. The next penny you pick will guarantee that you have at least five pennies from one of the years.
Therefore, you must pick a minimum of 12 + 1 = 13 pennies to be sure of getting at least five pennies from the same year.
Question
A penny collection contains twelve 1967 pennies, seven 1968 pennies, and eleven 1971 pennies. If you are to pick some pennies without looking at the dates, how many must your pick to be sure of getting at least five pennies from the same year?