Toss And Toss

When you flip a coin x amount of times, there will be $2^x$ unique solutions. This means that if you have $2^x$ people, you can flip a coin x amount of times. However, if you have more than $2^x$ people, you will need more than x coin flips.

In this case, there are $2050$ people. The closest power of $2$ is $2048=2^{11}$ . If there were $2048$ or less people, we could only do it will $11$ coin flips. However, because $2050$ is greater than $2^{11}$ , we need $12$ coin flips to determine the first person.

When we are determining the second person, we only have $2049$ people. It is still greater than $2^{11}$ , so we still need $12$ coin flips.

However, when choosing the third and final person, we only have $2048$ people, which is less than or equal to $2^{11}$ . Because of this, we only need $11$ coin flips to determine the third person.

Overall, we needed $12+12+11=35$ coin flips.