MathNet 2024-part-04 — 168 problems (EN–VI) Question 26

Milou has 100 long envelopes of different sizes. 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 organise the envelopes into piles. An envelope may only be placed on top of another envelope if both its width and height are smaller than that of the envelope she is placing it on. So the size $26 \times 15$ envelope is allowed on top of the $29 \times 17$ envelope, but not on the $29 \times 15$ envelope or the $26 \times 17$ envelope.
What is the smallest number of piles into which Milou can organise the envelopes?