The document shows that in any group of 80 people, at least 12 must have been born on the same day of the week. It uses a "pigeonhole principle" approach, imagining the days of the week as 7 bins. With 80 people distributed as widely as possible among the bins, each bin could hold up to 11 people, but the 78th person would require a 12th person be added to one of the bins. In reality, the bins are unlikely to hold exactly 11 people each, so a 12th person in a bin would occur earlier than the 78th person.
A Critique of the Proposed National Education Policy Reform
Show that in any group of 80 people, at least 12 were born onthe s.pdf
1. Show that in any group of 80 people, at least 12 were born onthe same day of the week.
Show that in any group of 80 people, at least 12 were born onthe same day of the week.
Solution
Imagine 7 bins (or "pigeonholes") -- one for each day of theweek. Further imagine that our
eighty poeple are are aswidely distributed across these bins as possible. Since 80/7= 11 r 3 we
could get up to 11 people in each bin for the first 77but when we add the 78th person, we'd have
to add a 12thperson to one of the bins. (In reality the first 77 peopleare very unlikely to be so
evenly distributed amoungst thepigeonholes and we're likely to have added a 12th to at least
onebin much earlier. )
(Edited for grammar and spelling.)
