The carillon on the courtyard plays a short piece every hour, starting at 8 and ending at 22. There are a total of eighteen pieces, and only one is played at each hour, and after all eighteen have been played, the cycle starts again in the same order. Olga and Libor were in the courtyard on Monday at 3 PM. Later that week, they came to listen to the carillon again at noon, to their disappointment, however, the same melody played that they heard on Monday.

On which day did Olga and Libor visit the courtyard for the second time?

(L. Simünek)

Hint. How many of the eighteen pieces will sound in one day and how many will not get a chance to play?
Between the first morning and the last evening composition, $22-8=14$ hours elapse, so fifteen compositions are played each day. The carillon has eighteen compositions set, which is three more.

The composition that the heroes of the story heard on Monday at 15:00 was played three hours later on Tuesday, at 18:00. On Wednesday, it was played another three hours later, at 21:00.

On Thursday, the observed composition did not sound at all: from the last time it was played, one of the seventeen other compositions was played on Wednesday at 22:00, fifteen on Thursday, one on Friday at 8:00, and the observed composition was played again at 9:00.

The next day, Saturday, the observed composition sounded three hours later, at 12:00. On Sunday, it sounded another three hours later, at 15:00.

During the given week, the observed composition played at noon only on Saturday, and Olga and Libor came to the courtyard for the second time on Saturday.

Note. The previous discussion can be replaced by the carillon program for the given week. Compositions are marked with numbers 1 to 18, where 1 represents the one heard by Olga and Libor:

|  | $8 \mathrm{~h}$ | $9 \mathrm{~h}$ | $10 \mathrm{~h}$ | $11 \mathrm{~h}$ | $12 \mathrm{~h}$ | $13 \mathrm{~h}$ | $14 \mathrm{~h}$ | $15 \mathrm{~h}$ | $16 \mathrm{~h}$ | $17 \mathrm{~h}$ | $18 \mathrm{~h}$ | $19 \mathrm{~h}$ | $20 \mathrm{~h}$ | $21 \mathrm{~h}$ | $22 \mathrm{~h}$ |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| Mon |  |  |  |  |  |  | $\ldots$ | $\mathbf{1}$ | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Tue | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | $\mathbf{1}$ | 2 | 3 | 4 | 5 |
| Wed | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | $\mathbf{1}$ | 2 |
| Thu | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
| Fri | 18 | $\mathbf{1}$ | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
| Sat | 15 | 16 | 17 | 18 | $\mathbf{1}$ | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| Sun | 12 | 13 | 14 | 15 | 16 | 17 | 18 | $\mathbf{1}$ | $\ldots$ |  |  |  |  |  |  |