Let p, q, r and s be natural numbers such that p - 2016 = q + 2017 = r - 2018 = s + 2019. Which one of the following is the largest natural number?

Let's assume the final result of all these equations is a fixed number, say $k$. We can visualize this as a race where everyone finishes at the same spot $k$.\n\n1. **Analyze the 'Plus' group ($q$ and $s$):**\n - $q + 2017 = k$ implies $q = k - 2017$.\n - $s + 2019 = k$ implies $s = k - 2019$.\n - These numbers are smaller than $k$ because we have to add something to them to reach $k$. So, $q$ and $s$ are out of the race for the 'largest' number.\n\n2. **Analyze the 'Minus' group ($p$ and $r$):**\n - $p - 2016 = k$ implies $p = k + 2016$.\n - $r - 2018 = k$ implies $r = k + 2018$.\n - These numbers are larger than $k$. We must choose between $p$ and $r$.\n\n3. **Compare $p$ and $r$:**\n - $p$ is $2016$ steps ahead of $k$.\n - $r$ is $2018$ steps ahead of $k$.\n - Since $2018 > 2016$, $r$ is clearly larger than $p$.\n\nUsing the 'Assumption Method' [28], if we set $k = 10,000$, then $p = 12,016$ and $r = 12,018$. Clearly, $r$ is the largest.