Carillon MO - Z5 - 1 - 66

The carillon in the courtyard plays at every full hour a short composition, starting at 8 a.m. and ending at 10 p.m. The compositions total eighteen, at the full hour always only one is played, and after playing all eighteen it starts again in the same order. Oľga and Ľuboš were at the courtyard on Monday at 3 p.m. The same week they came to listen to the carillon once more, at noon, but to their disappointment the same melody which they had heard on Monday was playing. Which day were Oľga and Ľuboš at the courtyard for the second time?

Final Answer:

x = Sobota

Step-by-step explanation:

$$\begin{gathered} a=15 \\ h=22-8+1=15 \\ {b}_1=a+18=15+18=33 \\ b=\mathrm{m}\mathrm{o}\mathrm{d}(b_1-8,h)+8=\mathrm{m}\mathrm{o}\mathrm{d}(33-8,15)+8=18 \\ {c}_1=b+18=18+18=36 \\ c=\mathrm{m}\mathrm{o}\mathrm{d}(c_1-8,h)+8=\mathrm{m}\mathrm{o}\mathrm{d}(36-8,15)+8=21 \\ {d}_1=c+18=21+18=39 \\ d=\mathrm{m}\mathrm{o}\mathrm{d}(d_1-8,h)+8=\mathrm{m}\mathrm{o}\mathrm{d}(39-8,15)+8=9 \\ {e}_1=d+18=9+18=27 \\ {e}_2=\mathrm{m}\mathrm{o}\mathrm{d}(e_1-8,h)+8=\mathrm{m}\mathrm{o}\mathrm{d}(27-8,15)+8=12 \\ {f}_1=e_2+18=12+18=30 \\ f=\mathrm{m}\mathrm{o}\mathrm{d}(f_1-8,h)+8=\mathrm{m}\mathrm{o}\mathrm{d}(30-8,15)+8=15 \\ x=Sobota \end{gathered}$$

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