Question 33
To make the separation in regions of the correspondence that must be delivered, a postal service indicates a postal code on the envelopes with a series of five groups of points and sticks, which can be read by an optical reader. In the normalized transcription below, $\mathtt0$ represents a point and $\mathtt1$ a rod. The digits are encoded as follows:
| $0:\ \mathtt{001111}$ | $5:\ \mathtt{101011}$ |
| --- | --- |
| $1:\ \mathtt{010111}$ | $6:\ \mathtt{101101}$ |
| $2:\ \mathtt{011011}$ | $7:\ \mathtt{110011}$ |
| $3:\ \mathtt{011101}$ | $8:\ \mathtt{110101}$ |
| $4:\ \mathtt{100111}$ | $9:\ \mathtt{111001}$ |
The reading is done from right to left. For example, postal code 91720 is written in blocks such as $\mathtt{001111\ 011011\ 110011\ 010111\ 111001}$:
Note that the encoding of $94$, that is, $\mathtt{100111\ 111001}$, has a vertical axis of symmetry. Find the codes from 47000 to 47999 that have a vertical axis of symmetry.
| $0:\ \mathtt{001111}$ | $5:\ \mathtt{101011}$ |
| --- | --- |
| $1:\ \mathtt{010111}$ | $6:\ \mathtt{101101}$ |
| $2:\ \mathtt{011011}$ | $7:\ \mathtt{110011}$ |
| $3:\ \mathtt{011101}$ | $8:\ \mathtt{110101}$ |
| $4:\ \mathtt{100111}$ | $9:\ \mathtt{111001}$ |
The reading is done from right to left. For example, postal code 91720 is written in blocks such as $\mathtt{001111\ 011011\ 110011\ 010111\ 111001}$:
Note that the encoding of $94$, that is, $\mathtt{100111\ 111001}$, has a vertical axis of symmetry. Find the codes from 47000 to 47999 that have a vertical axis of symmetry.