rough draft first guide

content/core.typ

@@ -84,6 +84,41 @@ We can't control the absolute entity ID a particular item will receive, but we c
 multiple entities. By observing the drop delay for a "reference" item, we can predict the behavior
 of other items.
 
+#example[
+  For example, suppose we spawn an item $A$, then 2 game ticks later we spawn an item $B$. Assume no
+  other entities spawn between them, so $A$ and $B$ have consecutive IDs. Wait for the items to
+  settle, then remove the supporting blocks. If we observe item $A$ start to fall 1 game tick after
+  the support is removed, we can predict when item $B$ will fall.
+
+  It'll be easier if we orient ourselves around the tick when the support blocks are removed, call
+  that $t=0$. Say the age is $"age"_(A, 0)$ at that time. We have that item $A$ falls at $t=1$.
+
+  $A$ fell when it was $"age"_(A, 1) = "age"_(A, 0) + 1$ old, so we can put all this into a relation
+  that pins down the mod 4 cycle.
+
+  $ "age"_(A, 0) + 1 + "id"_A equiv 0 (mod 4) $
+
+  We want to find the equivalent relation for $B$, where $x$ will be the tick in which $B$ falls.
+
+  $ "age"_(B, 0) + x + "id"_B equiv 0 (mod 4) $
+
+  We know that $A$ has the item ID immediately before $B$, so $"id"_A = "id"_B - 1$.
+
+  We also know that $A$ is 2gt older than $B$, so $"age"_(A, 0) = "age"_(B, 0) + 2$.
+
+  So take the relation for $A$ and substitute in these values for $B$.
+
+  $
+            "age"_(A, 0) + 1 + "id"_A & equiv 0 (mod 4) \
+    "age"_(B, 0) + 2 + 1 + "id"_B - 1 & equiv 0 (mod 4) \
+            "age"_(B, 0) + 2 + "id"_B & equiv 0 (mod 4) \
+  $
+
+  Compare with the relation for $B$ and we see that $x=2$.
+
+  #callout(kind: "tip", label: "Therefore:")[$B$ falls at time $t=2$.]
+]
+
 #example[
   Suppose we spawn four items in order. For simplicity, spawn them all in the same tick so their
   ages are equal, and assume no other entities spawn.

lib.typ

@@ -65,5 +65,4 @@
   }
 }
 
-// #let solution = details.with(label: "Solution")
-#let solution = callout.with(kind: "solution", label: "Solution:")
+#let solution = details.with(label: "Solution")