8000
Numbers are:
381 383 385 387 389 391 393 395 397 399 401 403 405 407 409 411 413 415 417 419
4
Odd numbers.
Alternating. 1 2 3 4 5 6 7 8 9 in row 3, (7,8,9) the 8 is even and the 7 and 9 are odd. thus odd,even,odd. in column 3, (3,6,9) the 6 is even and the 3 and 9 are odd, thus odd,even,odd. as the row/column selector (3) is odd the first digit in that row/column of a 3X3 grid will be odd as will the first. the numbers then alternate even odd even.
Sum of numbers in a nth row can be determined using the formula 2^n. For the 100th row, the sum of numbers is found to be 2^100=1.2676506x10^30.
without seeing the rows, nobody can answer the question.
4
If you consider row 0 as the row consisting of the single 1, then row 100 has 6 odd numbers.
The number of odd numbers in the Nth row of Pascal's triangle is equal to 2^n, where n is the number of 1's in the binary form of the N. In this case, 100 in binary is 1100100, so there are 8 odd numbers in the 100th row of Pascal's triangle.
Odd numbers.
8,000. each row's sum is the row # cubed. so the 20th row is 20*20*20 = 8000
The sum of the numbers on the fifteenth row of Pascal's triangle is 215 = 32768.
16020
The sum of the numbers in each row of Pascal's triangle is twice the sum of the previous row. Perhaps you can work it out from there. (Basically, you should use powers of 2.)
Alternating. 1 2 3 4 5 6 7 8 9 in row 3, (7,8,9) the 8 is even and the 7 and 9 are odd. thus odd,even,odd. in column 3, (3,6,9) the 6 is even and the 3 and 9 are odd, thus odd,even,odd. as the row/column selector (3) is odd the first digit in that row/column of a 3X3 grid will be odd as will the first. the numbers then alternate even odd even.
64
what is the pattern of odd and even number in each row
Let's calculate the sums of few first rows of Pascal's triangle: 1st row: 1 = 1 2nd row: 1 + 1 = 2 3rd row: 1 + 2 + 1 = 4 Looks promising, let's continue: 4th row: 1 + 3 + 3 + 1 = 8 5th row: 1 + 4 + 6 + 4 + 1 = 16 We can make an assumption that each row's sum is twice the sum of previous row - it's a power of two. But why is that? If you know how Pascal's triangle is constructed, you should notice that when creating new row, you use the previous row numbers(except ones) two times in addition. Considering ones, you only use each 1 in previous row once, but in the new row you always add two 1's on the sides. Alternatively, you may think of empty space around Pascal's triangle as zeros and then you'll definitely use each previous row's numbers two times to create a new row. The formula will be then: s = 2n-1, where s - sum of the nth row(we assume numeration starts with 1 for the single '1' on the top) n - number of the row