diff --git a/src/koans/equalities.clj b/src/koans/equalities.clj
index 025bec7..9d4a6af 100644
--- a/src/koans/equalities.clj
+++ b/src/koans/equalities.clj
@@ -18,4 +18,4 @@
   (== 2.0 2 __)
 
   "When things cannot be equal, they must be different"
-  (not= nil __))
+  (not= :fill-in-the-blank __))
diff --git a/src/koans/recursion.clj b/src/koans/recursion.clj
index 6cd34ba..7b7b6f1 100644
--- a/src/koans/recursion.clj
+++ b/src/koans/recursion.clj
@@ -1,5 +1,6 @@
 (defn is-even? [n]
-  (if (= n 0) __
+  (if (= n 0)
+      __
       (___ (is-even? (dec n)))))
 
 (defn is-even-bigint? [n]
@@ -33,7 +34,7 @@
   (= 24 (factorial 4))
 
   "You can even deal with very large numbers"
-  (= (factorial 1000N) (factorial 1000N))
+  (< 1000000000000000000000000N (factorial 1000N))
 
   "But what happens when the machine limits you?"
-  (= (factorial 10000N) (factorial 10000N)))
+  (< 1000000000000000000000000N (factorial 10000N)))
diff --git a/src/koans/vectors.clj b/src/koans/vectors.clj
index dcf8337..9397378 100644
--- a/src/koans/vectors.clj
+++ b/src/koans/vectors.clj
@@ -30,4 +30,4 @@
   (= __ (subvec [:peanut :butter :and :jelly] 1 3))
 
   "Equality with collections is in terms of values"
-  (___ (list 1 2 3) (vector 1 2 3)))
+  (= (list 1 2 3) (vector 1 2 __)))
diff --git a/src/path_to_answer_sheet.clj b/src/path_to_answer_sheet.clj
index ab2c642..b4b1348 100644
--- a/src/path_to_answer_sheet.clj
+++ b/src/path_to_answer_sheet.clj
@@ -30,8 +30,8 @@
                     :peanut
                     :jelly
                     :jelly
-                    [:butter :and]]
-              "___" ['=]}
+                    [:butter :and]
+                    3]}
    "sets" {"__" [3
                  #{1 2 3 4 5}
                  #{1 2 3 4 5}