B1. Milou has 100 long rectangular envelopes of different formats. Each envelope has a width equal to one of the integers $21, \ldots, 30$ and a height equal to one of the integers $11, \ldots, 20$, and each combination occurs exactly once. Milou wants to sort the envelopes into piles. An envelope can only be placed on another envelope if both the width and the height are smaller than those of the envelope it is placed on. The envelope of size $26 \times 15$ can thus be placed on that of $29 \times 17$, but not on that of $29 \times 15$ or that of $26 \times 17$. What is the smallest number of piles in which Milou can sort the envelopes?
B1. 19 An envelope with width 30 cannot fit into any other envelope, and an envelope with height 20 cannot fit into any other envelope either. Therefore, for the envelopes with dimensions $21 \times 20, 22 \times 20, \ldots, 30 \times 20, 30 \times 19, \ldots, 30 \times 11$, Milou must create 19 different stacks, with these envelopes at the bottom. We can see that the rest of the envelopes can all be placed on top of these as follows. Calculate the difference between the width $b$ and the height $h$ for each envelope. This difference is equal to a number from 1 to 19, and for all 19 envelopes that Milou has already placed, each difference occurs exactly once. All envelopes for which $b-h$ is the same can fit into the same stack. The stack for $b-h=5$, for example, looks like this from bottom to top: $25 \times 20, 24 \times 19, 23 \times 18, 22 \times 17$, and $21 \times 16$. Milou can thus place all the envelopes in 19 stacks, and fewer stacks are impossible.