In the basket 7

In the basket there are blue, green, purple, and red balls. Tomáš, Peter, and Jakub can distinguish colours but confuse their names. One of them confuses blue colour with green, the second green with purple colour, and the third mistook purple with red. Thus each of them wrote a different list of colours located in the basket. How many purple balls are there?
Tomáš wrote 1 blue, 3 green, 5 purple and 7 red
Peter wrote 1 blue, 5 green, 7 purple and 3 red
Jakub wrote 5 blue, 1 green, 3 purple and 7 red

Final Answer:

f =  3

Step-by-step explanation:

$$\begin{gathered} M\nexists Z \\ Z\nexists F \\ F\nexists C \\ J:M\nexists Z,z=5m=1f=3c=7 \\ P:F\nexists C,m=1z=5,f=3c=7 \\ T:Z\nexists F,m=1f=3z=5,c=7 \\ f=3 \end{gathered}$$

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