Hens and pigs

Hens and pigs have 46 feet in total. At least how much can heads have?

Result

n =  12

Solution:

$46=2s+4p \ \\ p=46/4=\dfrac{ 23 }{ 2 }=11.5 \ \\ \ \\ p_{1}=\lfloor p \rfloor=\lfloor 11.5 \rfloor=11 \ \\ s_{1}=(46 - 4 \cdot \ p_{1})/2=(46 - 4 \cdot \ 11)/2=1 \ \\ \ \\ n=s_{1}+p_{1}=1+11=12$

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