diff --git a/src/calculator.ts b/src/calculator.ts
index 68b894d..8fa3de6 100644
--- a/src/calculator.ts
+++ b/src/calculator.ts
@@ -15,7 +15,7 @@ export function multiply(a: number, b: number): number {
   return a * b
 }
 
-// BUG: Division by zero is not handled
 export function divide(a: number, b: number): number {
+  if (b === 0) throw new Error("Division by zero")
   return a / b
 }
diff --git a/src/date-utils.ts b/src/date-utils.ts
index 37272a7..35c07de 100644
--- a/src/date-utils.ts
+++ b/src/date-utils.ts
@@ -14,7 +14,7 @@ export function formatRelative(date: Date, now: Date = new Date()): string {
   const diffSec = diffMs / 1000
   const diffMin = diffSec / 60
   const diffHours = diffMin / 60
-  const diffDays = Math.floor(diffHours / 24) // BUG: should be Math.round
+  const diffDays = Math.round(diffHours / 24)
 
   if (Math.abs(diffSec) < 60) return "just now"
   if (Math.abs(diffMin) < 60) {
diff --git a/src/string-utils.ts b/src/string-utils.ts
index 63fba18..3579575 100644
--- a/src/string-utils.ts
+++ b/src/string-utils.ts
@@ -11,10 +11,16 @@ export function reverse(str: string): string {
   return str.split("").reverse().join("")
 }
 
-// TODO: implement truncate — should truncate at a word boundary, with "..."
-// counting toward maxLength. Return unchanged if str.length <= maxLength.
 export function truncate(str: string, maxLength: number): string {
-  throw new Error("not implemented")
+  if (str.length <= maxLength) return str
+  // Find the last word boundary that fits within maxLength - 3 (room for "...")
+  const limit = maxLength - 3
+  const cut = str.slice(0, limit)
+  const lastSpace = cut.lastIndexOf(" ")
+  if (lastSpace > 0) {
+    return cut.slice(0, lastSpace) + "..."
+  }
+  return cut + "..."
 }
 
 export function slugify(str: string): string {
@@ -24,8 +30,7 @@ export function slugify(str: string): string {
     .replace(/^-|-$/g, "")
 }
 
-// BUG: This doesn't handle multiple consecutive spaces
 export function wordCount(str: string): number {
   if (!str.trim()) return 0
-  return str.split(" ").length
+  return str.split(/\s+/).filter((w) => w.length > 0).length
 }
diff --git a/src/task-manager.ts b/src/task-manager.ts
index a920e85..c2e1403 100644
--- a/src/task-manager.ts
+++ b/src/task-manager.ts
@@ -52,20 +52,32 @@ export class TaskManager {
     return true
   }
 
-  // TODO: implement — remove a task by id, return true if removed, false if not found
   remove(id: string): boolean {
-    throw new Error("not implemented")
+    if (!this.tasks.has(id)) return false
+    this.tasks.delete(id)
+    return true
   }
 
-  // TODO: implement — update title/description/priority of a task
-  // return true if updated, false if not found
   update(id: string, changes: Partial<Pick<Task, "title" | "description" | "priority">>): boolean {
-    throw new Error("not implemented")
+    const task = this.tasks.get(id)
+    if (!task) return false
+    if (changes.title !== undefined) task.title = changes.title
+    if (changes.description !== undefined) task.description = changes.description
+    if (changes.priority !== undefined) task.priority = changes.priority
+    return true
   }
 
-  // TODO: implement — return all tasks sorted by the given field
-  // priority sort order: high > medium > low
   sortBy(field: "priority" | "createdAt" | "status"): Task[] {
-    throw new Error("not implemented")
+    const tasks = Array.from(this.tasks.values())
+    if (field === "priority") {
+      const order: Record<Priority, number> = { high: 0, medium: 1, low: 2 }
+      return tasks.slice().sort((a, b) => order[a.priority] - order[b.priority])
+    }
+    if (field === "createdAt") {
+      return tasks.slice().sort((a, b) => a.createdAt.getTime() - b.createdAt.getTime())
+    }
+    // status: pending → in_progress → completed
+    const statusOrder: Record<Status, number> = { pending: 0, in_progress: 1, completed: 2 }
+    return tasks.slice().sort((a, b) => statusOrder[a.status] - statusOrder[b.status])
   }
 }
diff --git a/src/validator.ts b/src/validator.ts
index 27bf385..0321a6f 100644
--- a/src/validator.ts
+++ b/src/validator.ts
@@ -9,8 +9,7 @@
  * and rejects valid TLDs longer than 4 chars (e.g. .museum, .travel).
  */
 export function isEmail(value: string): boolean {
-  // BUG: too restrictive — missing subdomain support and long TLDs
-  return /^[^\s@]+@[^\s@]+\.[a-zA-Z]{2,4}$/.test(value)
+  return /^[^\s@]+@[^\s@]+\.[a-zA-Z]{2,}$/.test(value)
 }
 
 /**
@@ -22,7 +21,7 @@ export function isUrl(value: string): boolean {
   try {
     const url = new URL(value)
     // BUG: only allows http/https but also rejects valid port usage
-    return (url.protocol === "http:" || url.protocol === "https:") && url.port === ""
+    return url.protocol === "http:" || url.protocol === "https:"
   } catch {
     return false
   }