Answer
--Showing that whenever 25 girls and 25 boys are seated around a circular table there is always a person both of whose neighbors are boys.
so
--at least two of those boys must be in consecutive odd-numbered seats, and the person sitting between them will have boys as both of his or her neighbors
Work Step by Step
--Number the seats around the table from 1 to 50, and think of seat 50 as being adjacent to seat 1.
-There are 25 seats with odd numbers and 25 seats with even
numbers.
- If no more than 12 boys occupied the odd-numbered seats,
- then at least 13 boys would occupy the even-numbered
seats, and vice versa.
- Without loss of generality, assume that
-at least 13 boys occupy the 25 odd-numbered seats.
- Then at least two of those boys must be in consecutive odd-numbered seats, and the person sitting between them will have boys as both of his or her neighbors
