Galactophone

Grandma Šebestová decided to pass on her secret recipe for gingerbread spice to her 10 grandchildren. And since she is a great trickster, she decided to make it a bit more complicated for them. To each grandchild she sent an old-fashioned paper letter with the name of exactly one of the exactly 10 ingredients of her secret gingerbread spice. Each of the grandchildren, however, wanted to know the entire recipe, so they needed to exchange their information. Each grandchild had a galactophone (abbreviation for galactic portable telephone) and can call each other. In the conversation they of course always tell each other everything they have learned. Is it possible that every grandchild would find out all 10 ingredients and that they would need for this together less than 18 calls? Please justify your claim.

Final Answer:

n =  45

Step-by-step explanation:

$$\begin{gathered} n=10\cdot (10-1)/2=45 \\ n>18 \end{gathered}$$

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