How many odd numbers are there in row 255 of pascals triangle?

Answer 1

In Pascal's Triangle, the entries in row ( n ) correspond to the binomial coefficients ( \binom{n}{k} ) for ( k = 0, 1, 2, \ldots, n ). The number of odd numbers in row ( n ) can be determined using the binary representation of ( n ). For row 255, which is ( 255_{10} = 11111111_2 ) in binary, the number of odd entries is given by ( 2^k ), where ( k ) is the number of 1's in the binary representation. Since there are 8 ones in the binary representation of 255, there are ( 2^8 = 256 ) odd numbers in row 255 of Pascal's Triangle.