Talk:2011 AMC 10B Problems/Problem 23

I don't get the Pascal's Triangle solution. I did it using Pascal's triangle, but I had more steps, I didn't do it like that. How did you ignore the tens digit and get the right answer?

Pascal's Triangle Solution

Be aware that the 2000 in 2011 doesn't contribute to the hundreds digit of the power. The question is then simplified into finding the hundreds digit of /Users/hourosemary/Desktop/截屏2025-08-31 20.47.37.png. Then, we need to find out the last 3 numbers in the 2012th row of the Pascal's triangle. By the Pascal's triangle, we have:

/Users/hourosemary/Desktop/截屏2025-08-31 20.33.01.png

By this we know that the last three numbers of the 2012th row are /Users/hourosemary/Desktop/截屏2025-08-31, 20.36.05.png/Users/hourosemary/Desktop/截屏2025-08-31 20.36.56.png, and 1. The calculations are 2021055, 2011, and 1. We need the units digit of the first number and the tens digit of the second number, so we do 5+1= /Users/hourosemary/Desktop/2c024459b191f13b58f34b5e366d4e49e32cad7c.png.