lessons: add two new list opt lessons

lessons/list-optimizations/0004-list-optimizations-find-a-pattern-easy.md

@@ -0,0 +1,35 @@
+# Find a Pattern (easy)
+List constants often have patterns. Ask "what do the elements of this list have in common?" or "can I express this as a sequence?".
+
+_Hint: Remember that the color constants are just numbers. What operations can you do on lists of numbers?_
+
+```json
+{
+  "id": 4,
+  "name": "List Optimizations: Find a Pattern (easy)",
+  "requirements": [3],
+  "starting_program": "{RED,ORANGE,YELLOW,GREEN,BLUE,MAGENTA->L1\n{0,3,24,81,192,375,648,1029->L2",
+  "required_savings": 20,
+  "tests": [
+    {
+      "regex": "10\\+{1,5,9,4,0,3->L1[\\n:]seq\\(3([A-Z]|theta)\\^\\^3,\\1,0,7->L2"
+    },
+    {
+      "regex": "seq\\(3([A-Z]|theta)\\^\\^3,\\1,0,7->L2[\\n:]10\\+{1,5,9,4,0,3->L1"
+    },
+    {
+      "input": [{"name": "L3", "value": [0,3,24,81,192,375,648,1029]}],
+      "output": [
+        {
+          "name": "L1",
+          "value": [11,15,19,14,10,13]
+        },
+        {
+          "name": "L2",
+          "value": [0,3,24,81,192,375,648,1029]
+        }
+      ]
+    }
+  ]
+}
+```

lessons/list-optimizations/0006-list-optimizations-binompdf.md

@@ -0,0 +1,42 @@
+# List Optimizations: `binompdf(`and`binomcdf(`
+In addition to their expected uses in probability and statistics, the `binompdf(` and `binomcdf(` commands are useful in TI-BASIC when generating certain special lists.
+
+Critically for optimization, `binompdf(N,0` produces a list with a single one, followed by N zeros. Also, in the two argument case, `binomcdf(` is, definitionally, `cumSum(binompdf(`.
+
+We can put these two facts together in interesting ways:
+- `cumSum(binomcdf(N,0` -> `{1,2,3,4,5,...,N+1`
+- `cumSum(not(binompdf(N,0` -> `{0,1,2,3,4,...,N`
+
+Expressing a sequence using `seq(` often takes more bytes than expressing the sequence using these techniques, especially if the trailing parentheses in the `binom` method can be pruned.
+
+```json
+{
+  "id": 6,
+  "name": "List Optimizations: binompdf( and binomcdf(",
+  "requirements": [4],
+  "starting_program": "15seq(X,X,1,10->L1\n{WHITE,LTGRAY,MEDGRAY,GRAY,DARKGRAY->L2",
+  "required_savings": 7,
+  "tests": [
+    [
+      {
+        "input": [],
+        "output": [
+          {
+            "name": "L1",
+            "value": [15,30,45,60,75,90,105,120,135,150]
+          }
+        ]
+      },
+      {
+        "input": [],
+        "output": [
+          {
+            "name": "L2",
+            "value": [20,21,22,23,24]
+          }
+        ]
+      }
+    ]
+  ]
+}
+```