B1. One card with '1', two cards with '2', three cards with '3', $\ldots$, fifty cards with '50'. Put all these $1+2+3+\cdots+50=1275$ cards in a box and mix them well. How many cards must you at least draw from the box to be sure that you have at least ten cards with the same number?
B1. Start from the worst-case scenario. Then you pick all the cards with a number from 1 to 9, and there are 45 of them. From all other cards, with numbers from 10 to 50, you pick nine cards with the same number each time. That makes $41 \times 9=369$. You have already picked a total of $45+369=414$ cards. If you pick $414+1=415$ cards, then there must be at least ten with the same number.