Question 1023154
{{{29 <= (31+41+p)/3 <= 47}}}
<==> {{{87 <= p+72 <= 141}}}
<==> {{{15 <= p <= 69}}}
<==> {{{8 <= p-7 <= 62}}}
==> {{{64 <= (p-7)^2 <= 3844}}}

The least possible value of {{{(p-7)^2}}} is now clear.