Calendar made of cubes

27

the location of the polygons adjacent to the vertex. For example, solution $m_3 = 1, m_4 = 2, m_6 = 1,$
$$\left(1 - \frac{2}{3}\right) + 2\left(1 - \frac{2}{4}\right) + \left(1 - \frac{2}{6}\right) = 2,$$

corresponds to the vertices at which one triangle, two squares and one hexagon meet. They can be easily arranged in two significantly different ways (Fig. 5, a and b). But it is easy to show (prove!) that arrangement 6 does not correspond to any regular parquet.

The indicated given is sufficient. Get to work!

Hocus Pocus

In Vyacheslav Shishkov’s novel “Strandiki” there are the following lines:

• Do you want me to show you arithmetic hocus pocus? You’ll gasp.
• Oh! Well, show me, milliny.
  Ivan Petrovich tore a page out of the notebook, handed it to the boy, and asked:
• Do you have a pencil? Write any number.
  The boy wrote. Ivan Petrovich looked at this number in chalk, wrote his own number on a separate key of paper, put the piece of paper in the straw and covered it with his hat.
• Write something else under it. Pissed? Now I’ll write the third one myself. Now all three numbers are added. Just be more careful, don’t lie.
  Two minutes later the verified answer was ready. Engineer Voshkin submitted his calculations:

46 853
21 398
78 601
146 852

• One hundred and forty-six thousand eight hundred and fifty-two, Ivan Petrovich.
• You’ve been counting for a long time. And here is my answer. I already knew it when you wrote the first number. Here. Pull from under the hat.
  The boy grabbed the piece of paper. It read: 146,852. Engineer Voshkin’s surprised face stretched out, and the hair on the back of his neck stood up. With wealth, with surprise, he stared at Ivan Petrovich
• Well… so… how? … A?..
  Ivan Petrovich, smiling and moving his eyebrows, explained twice and gave another example…”
  The question is, what was Ivan Petrovich explaining, “smiling and moving his eyebrows”?

Such a calendar, made up of two cubes, is on the table in our editorial office. Think about how it is made: what numbers and how should they be glued on the faces of the cubes so that the calendar can show any day of the month? It is clear that there may be several answers. How much do you think?