Sponsor

The children of the tennis school received 64 white and 48 yellow balls from the sponsor. When asked about how many balls they could take, they were answered: "You have so many that none of you will have more than 10 balls and all will have the same number white and yellow balls. How many children were in the tennis school?

Correct result:

n =  16

Solution:

$$\begin{gathered} 64=2^6 \\ 48=2^4\cdot 3 \\ \text{GCD}(64,48)=2^4=16 \\ n=GCD(64,48)=16 \\ m=(64+48)\mathrm{/}n=(64+48)\mathrm{/}16=7 \\ m<10 \\ n=16 \end{gathered}$$

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