B2. From a set of 50 different numbers from the collection $\{1,2,3, \ldots, 100\}$, the sum is equal to 2900. What is the smallest possible number of even numbers among these 50 numbers?
B2. 6 If you take all 50 odd numbers from the set $\{1,2,3, \ldots, 100\}$, their sum is $\frac{1}{2} \times 50 \times(1+99)=2500$. That is 400 too little. Therefore, replace the smallest odd numbers with the largest possible even numbers, each time in pairs because 400 is even. If we replace 1 and 3 with 100 and 98, we get 2694. Then $2694-5-7+96+94=2872$. We need to do at least one more such step. And that works: $2872-9-11=2852$, so replace, for example, 20 and 28; then we have found a sum of 2900 with 6 even numbers and we have also shown that it cannot be done with fewer.