Question 21
Four positive integers $a,$ $b,$ $c,$ and $d$ have a product of $8!$ and satisfy
$$
ab + a + b = 524,
$$$$
bc + b + c = 146,
$$$$
cd + c + d = 104.
$$
What is $a - d?$
$$
ab + a + b = 524,
$$$$
bc + b + c = 146,
$$$$
cd + c + d = 104.
$$
What is $a - d?$