Z7-1-6 MO 2017

The water sprite Chaluha was pouring fog into various differently sized vessels, which he had carefully arranged on a shelf. When pouring, he proceeded gradually from one side, skipping no vessel. Into each vessel at least a decilitre of fog fits. If he were pouring fog with a seven-litre measuring cup, the fog from the first measuring cup would fill exactly 11 vessels, the fog from the second measuring cup would fill exactly another 12 vessels, and the fog from the third measuring cup would fill exactly 7 vessels. If he used a five-litre measuring cup, then the fog from the first measuring cup would fill exactly 8 vessels, from the second exactly 10 vessels, from the third exactly 7 vessels, and from the fourth measuring cup exactly 4 vessels. Decide whether the thirtieth vessel in order is larger than the twenty-fifth.

Final Answer:

x =  30

Step-by-step explanation:

$$\begin{gathered} t_1=7\cdot 3=21\text{l} \\ {t}_2=5\cdot 4=20\text{l} \\ {V}_1+V_2+\dots +V_8=5l \\ {V}_9+V_{10}+V_{11}=7-5=2l \\ {V}_{12}+\dots +V_{18}=3l \\ {V}_{19}+\dots +V_{23}=4l \\ {V}_{24}+V_{25}=1l \\ {V}_{25}+\dots +V_{29}=5l \\ {V}_{30}=1l \\ {V}_{24}+V_{25}=1l \\ {V}_{25}=1-V_{24} \\ {V}_{30}>V_{25} \\ x=30 \end{gathered}$$

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