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diff --git a/exercises/assignment3_answers.mdwn b/exercises/assignment3_answers.mdwn
index 7530534f..ae35731b 100644
--- a/exercises/assignment3_answers.mdwn
+++ b/exercises/assignment3_answers.mdwn
@@ -167,7 +167,7 @@ where `one` abbreviates `succ zero`, and `two` abbreviates `succ (succ zero)`.
     >      let leq? = \l r. zero? (sub l r) in
     >      ...
 
-    > Here is another solution. Jim crafted this particular implementation, but like a great deal of the CS knowledge he's gained over the past eight years, Oleg Kiselyov pointed the way.
+    > Here is another solution. Jim crafted this particular implementation, but like a great deal of the CS knowledge he's gained over the past eight years, Oleg Kiselyov pointed the way. <!-- see "lambda-calc-opposites.txt" at http://okmij.org/ftp/Computation/lambda-calc.html#neg -->
 
     >     let leq? = (\base build consume. \l r. r consume (l build base) fst)
     >             ; where base is
@@ -238,23 +238,6 @@ Reduce the following forms, if possible:
 Using the mapping specified in this week's notes, translate the following lambda terms into combinatory logic:
 
 
-
-Let's say that for any lambda term T, [T] is the equivalent Combinatory Logic term. Then we define the [.] mapping as follows.
-
- 1. [a]          =   a
- 2. [(\aX)]      =   @a[X]
- 3. [(XY)]       =   ([X][Y])
-
-Wait, what is that @a ... business? Well, that's another operation on (a variable and) a CL expression, that we can define like this:
-
- 4. @aa          =   I
- 5. @aX          =   KX           if a is not in X
- 6. @a(Xa)       =   X            if a is not in X
- 7. @a(XY)       =   S(@aX)(@aY)
-
-
-
-
 <ol start=19>
 <li><code>[\x x] = @x x = I</code>
 <li><code>[\x y. x] = @x [\y. x] = @x. (@y x) = @x (Kx) = S (@x K) (@x x) = S (KK) I</code>; in general expressions of this form <code>S(K<i>M</i>)I</code> will behave just like <code><i>M</i></code> for any expression <code><i>M</i></code>
@@ -284,6 +267,12 @@ S (S (KS) (S (KK) (S (KS) K))) (KI)</code>; this is the <b>B</b> combinator, whi
 
 25. For each of the above translations, how many `I`s are there? Give a rule for describing what each `I` corresponds to in the original lambda term.
 
+    This generalization depends on you omitting the translation rule:
+
+        6. @a(Xa)       =   X            if a is not in X
+
+    > With that shortcut rule omitted, then there turn out to be one `I` in the result corresponding to each occurrence of a bound variable in the original term.
+
 Evaluation strategies in Combinatory Logic
 ------------------------------------------
 
@@ -323,8 +312,8 @@ Reduce to beta-normal forms:
 <OL start=30>
 <LI><code>(\x. x (\y. y x)) (v w) ~~> v w (\y. y (v w))</code>
 <LI><code>(\x. x (\x. y x)) (v w) ~~> v w (\x. y x)</code>
-<LI><code>(\x. x (\y. y x)) (v x) ~~> v w (\y. y (v x))</code>
-<LI><code>(\x. x (\y. y x)) (v y) ~~> v w (\u. u (v y))</code>
+<LI><code>(\x. x (\y. y x)) (v x) ~~> v x (\y. y (v x))</code>
+<LI><code>(\x. x (\y. y x)) (v y) ~~> v y (\u. u (v y))</code>
 
 <LI><code>(\x y. x y y) u v ~~> u v v</code>
 <LI><code>(\x y. y x) (u v) z w ~~> z (u v) w</code>