Brain Teaser

When Fred graduated from high school in May 1993, after having celebrated his 18th birthday in March,

he received a small check from his grandma. Being a frugal sort, he decided that the best thing to spend

his money on would be something that he could use for the rest of his life, even if he lived to be 124:

calendars. He figured that as long as he never wrote on them, and he didn't care about the more

irregular holidays like Easter, he could use and reuse a set of calendars until he died. He had a calendar

for every year since the year he was born, so he knew he wouldn't have to buy too many more. He did

want to maximize his space though, so he decided to get rid of any of the ones that he already had that

he didn't need. He would just buy the remaining ones that he would need as time wore on.

Can you figure out how many calendars he got rid of, how many he would need in total, and how many

years it took him to finish his collection? Assume that he doesn't die before completing his collection, and

that he won't buy a new one until January 1st of the year in question.