diff --git a/.gitignore b/.gitignore
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+++ b/.gitignore
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+__pycache__
+*/Cargo.lock
+*/target/*
diff --git a/__pycache__/insert_digit_anywhere.cpython-38.pyc b/__pycache__/insert_digit_anywhere.cpython-38.pyc
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diff --git a/non_squarefree/Cargo.toml b/non_squarefree/Cargo.toml
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+++ b/non_squarefree/Cargo.toml
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+[package]
+name = "non_squarefree"
+version = "0.1.0"
+authors = ["William Ball <wball1@swarthmore.edu>"]
+edition = "2018"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]
+primal = "0.3.0"
diff --git a/non_squarefree/src/main.rs b/non_squarefree/src/main.rs
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+/* An attempt to see if you can walk to infinity on non-squarefree numbers
+ * The answer is a very obvious "yes" I should have seen coming.
+ * 4 -> 44 -> 444 -> 4444 -> ...
+ * will always be divisible by 4 and thus will always be non-squarefree
+ * Similarly
+ * 9 -> 99 -> 999 -> 9999 -> ...
+ * will always be divisible by 9.
+ */
+
+use std::collections::HashMap;
+
+#[derive(Debug)]
+struct Tree {
+    value: u64,
+    children: Vec<Tree>,
+}
+
+impl Tree {
+    fn new(value: u64, children: Vec<u64>) -> Tree {
+        let mut tree_children = Vec::with_capacity(children.len());
+        for child in children {
+            tree_children.push(Tree::new(child, Vec::new()));
+        }
+        Tree {
+            value,
+            children: tree_children,
+        }
+    }
+
+    fn step(&mut self, square_free: &mut HashMap<u64, bool>) {
+        if self.children.is_empty() {
+            let xs = step_end(self.value, square_free);
+            for val in xs {
+                self.children.push(Tree::new(val, Vec::new()));
+            }
+            return;
+        }
+        for child in &mut self.children {
+            child.step(square_free);
+        }
+    }
+
+    fn longest_path(&self) -> Vec<u64> {
+        if self.children.is_empty() {
+            return vec![self.value];
+        }
+        let mut max_path = vec![];
+        let mut max_length = 0;
+        for child in &self.children {
+            let temp = child.longest_path();
+            if temp.len() > max_length {
+                max_length = temp.len();
+                max_path = temp;
+            }
+        }
+        let mut retval = vec![self.value];
+        retval.append(&mut max_path);
+        return retval;
+    }
+
+    fn to_string(&self) -> String {
+        let mut retval = format!("[{}: ", self.value);
+        for child in &self.children {
+            retval.push_str(&child.to_string()[..]);
+        }
+        retval.push(']');
+        retval
+    }
+
+    fn count(&self) -> usize {
+        if self.children.is_empty() {
+            return 1;
+        }
+        return self.children.iter().fold(0, |mut sum, x| { sum += x.count(); sum });
+    }
+}
+
+fn step_end(x: u64, square_free: &mut HashMap<u64, bool>) -> Vec<u64> {
+    let mut new_xs = Vec::new();
+    for d in 0..10 {
+        let temp = x * 10 + d;
+        if !is_squarefree(temp, square_free) {
+            new_xs.push(temp);
+        }
+    }
+    return new_xs;
+}
+
+fn is_squarefree(n: u64, square_free: &mut HashMap<u64, bool>) -> bool {
+    match square_free.get(&n) {
+        Some(val) => *val,
+        None => {
+            let n = n as usize;
+            for prime in primal::Primes::all().take(n) {
+                if n % (prime * prime) == 0 {
+                    return false;
+                }
+            }
+            true
+        }
+    }
+}
+
+fn main() {
+    let mut tree = Tree::new(0, vec![4, 9]);
+    let mut square_free: HashMap<u64, bool> = HashMap::new();
+    for _ in 0..10 {
+        tree.step(&mut square_free);
+        println!("{:?}", tree.longest_path());
+        println!("{}", tree.count());
+    }
+    println!("{:?}", tree.to_string());
+}