diff --git a/examples/sumcheck.rs b/examples/sumcheck.rs
index 9917cfc..095dbff 100644
--- a/examples/sumcheck.rs
+++ b/examples/sumcheck.rs
@@ -23,7 +23,7 @@ where
     fn add_sumcheck(mut self, num_var: usize) -> Self {
         for _ in 0..num_var {
             self = self
-                .add_scalars(2, "partial evaluation")
+                .add_scalars(1, "partial evaluation, constant term")
                 .challenge_scalars(1, "sumcheck challenge");
         }
         self = self.add_scalars(1, "folded polynomial");
@@ -43,9 +43,9 @@ where
     let mut partial_poly = polynomial.clone();
     for _ in 0..num_var {
         let eval = partial_poly.to_evaluations();
+        // The partial polynomial of each round is of the form b * x + a.
         let a = eval.iter().step_by(2).sum();
-        let b = eval.iter().skip(1).step_by(2).sum();
-        merlin.add_scalars(&[a, b])?;
+        merlin.add_scalars(&[a])?;
         let [r] = merlin.challenge_scalars()?;
         partial_poly = partial_poly.fix_variables(&[r]);
     }
@@ -67,12 +67,10 @@ where
     let mut value = value.clone();
     let num_vars = polynomial.num_vars();
     for _ in 0..num_vars {
-        let [a, b] = arthur.next_scalars()?;
-        if a + b != value {
-            return Err(ProofError::InvalidProof);
-        }
+        let [a] = arthur.next_scalars()?;
+        let b = value - a - a;
         let [r] = arthur.challenge_scalars()?;
-        value = (b - a) * r + a;
+        value = b * r + a;
     }
     let [folded] = arthur.next_scalars()?;
     if folded != value {
@@ -84,11 +82,10 @@ where
 
 fn main() {
     use ark_curve25519::Fq;
-    use rand::rngs::OsRng;
     use ark_poly::DenseMultilinearExtension;
+    use rand::rngs::OsRng;
 
-    let num_vars= 4;
-
+    let num_vars = 4;
 
     // initialize the IO Pattern putting the domain separator ("example.com")
     let iopattern = IOPattern::new("example.com");