diff --git a/src/money/cents.ts b/src/money/cents.ts
index f6321d8..a5f5cde 100644
--- a/src/money/cents.ts
+++ b/src/money/cents.ts
@@ -29,22 +29,23 @@ export function parseCents(input: string): number {
 /**
  * Split an integer amount of cents evenly across member ids.
  *
- * SEEDED DEFECT (issue #2): this floors every share and drops the
- * remainder instead of handing the leftover cents to the first N members,
- * so the shares can sum to less than totalCents. `bun test` does not catch
- * this because the baseline tests only split amounts that divide evenly.
- * The correct remainder rule is documented in
- * .claude/skills/handling-money/references/rules.md.
+ * Remainder rule (.claude/skills/handling-money/references/rules.md): every
+ * member gets floor(totalCents / n), and the first `remainder` members, in
+ * the order passed in, get one extra cent, so the shares always sum to
+ * exactly totalCents. Negative or non-integer totals are out of scope for
+ * the rule and keep the plain floored share, unchanged from before.
  */
 export function splitCents(totalCents: number, memberIds: string[]): Record<string, number> {
   if (memberIds.length === 0) {
     throw new Error("cannot split among zero members");
   }
-  const share = Math.floor(totalCents / memberIds.length);
+  const base = Math.floor(totalCents / memberIds.length);
+  const remainder =
+    Number.isInteger(totalCents) && totalCents >= 0 ? totalCents - base * memberIds.length : 0;
   const shares: Record<string, number> = {};
-  for (const id of memberIds) {
-    shares[id] = share;
-  }
+  memberIds.forEach((id, i) => {
+    shares[id] = i < remainder ? base + 1 : base;
+  });
   return shares;
 }
 
diff --git a/tests/money.test.ts b/tests/money.test.ts
index ed1ee3f..b4351a9 100644
--- a/tests/money.test.ts
+++ b/tests/money.test.ts
@@ -36,4 +36,34 @@ describe("splitCents", () => {
     const shares = splitCents(2000, ["a", "b"]);
     expect(sumCents(Object.values(shares))).toBe(2000);
   });
+
+  test("gives the remainder cents to the first members", () => {
+    expect(splitCents(1000, ["a", "b", "c"])).toEqual({ a: 334, b: 333, c: 333 });
+  });
+
+  test("shares always sum to the total", () => {
+    const cases: Array<[number, number]> = [
+      [1000, 3],
+      [101, 5],
+      [1, 3],
+      [2, 3],
+      [999, 7],
+      [1003, 4],
+    ];
+    for (const [total, n] of cases) {
+      const ids = Array.from({ length: n }, (_, i) => `m${i}`);
+      const shares = splitCents(total, ids);
+      expect(sumCents(Object.values(shares))).toBe(total);
+      const base = Math.floor(total / n);
+      const remainder = total - base * n;
+      ids.forEach((id, i) => {
+        expect(shares[id]).toBe(i < remainder ? base + 1 : base);
+      });
+    }
+  });
+
+  test("leaves negative and non-integer totals floored as before", () => {
+    expect(splitCents(-1000, ["a", "b", "c"])).toEqual({ a: -334, b: -334, c: -334 });
+    expect(splitCents(10.5, ["a", "b"])).toEqual({ a: 5, b: 5 });
+  });
 });