<s>[INST] A scientist measured the lengths of 1000 dominoes in millimeters, as part of his research in physics. We don't have the actual measurements but are given a useful fact: if there are $n$ dominoes that measure $m$ millimeters, there are less than 70 times as many $(n-1)$ dominoes that are 1 millimeter longer, for all $n$ and $m$.
Let $d(m)$ be the number of dominoes of length $m$. Then the condition is $d(m+1) < 70d(m)$ for all $m$. Assume $d(3) = 20$.
What is the ratio of the number of dominoes that are 4 millimeters long to the number that are 3 millimeters long?[/INST]