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..4aad361 100644
--- a/src/date-utils.ts
+++ b/src/date-utils.ts
@@ -5,16 +5,13 @@
 /**
  * Format a date as a human-readable relative string.
  * e.g. "2 days ago", "just now", "in 3 hours"
- *
- * BUG: off-by-one — uses Math.floor where Math.round is needed for days,
- * causing "1 day ago" to appear for anything from 12h to 47h.
  */
 export function formatRelative(date: Date, now: Date = new Date()): string {
   const diffMs = now.getTime() - date.getTime()
   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(Math.abs(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..36f8f70 100644
--- a/src/string-utils.ts
+++ b/src/string-utils.ts
@@ -11,10 +11,24 @@ 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.
+const ELLIPSIS = "..."
+
+/**
+ * Truncate a string to at most `maxLength` characters, cutting at a word
+ * boundary and appending "...". The ellipsis counts toward `maxLength`.
+ * Returns the string unchanged when it already fits.
+ */
 export function truncate(str: string, maxLength: number): string {
-  throw new Error("not implemented")
+  if (str.length <= maxLength) return str
+
+  const budget = maxLength - ELLIPSIS.length
+  if (budget <= 0) return str.slice(0, Math.max(0, maxLength))
+
+  const head = str.slice(0, budget)
+  const lastSpace = head.lastIndexOf(" ")
+  const body = lastSpace > 0 ? head.slice(0, lastSpace) : head
+
+  return body + ELLIPSIS
 }
 
 export function slugify(str: string): string {
@@ -24,8 +38,8 @@ 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
+  const trimmed = str.trim()
+  if (!trimmed) return 0
+  return trimmed.split(/\s+/).length
 }
diff --git a/src/task-manager.ts b/src/task-manager.ts
index a920e85..c3cb05c 100644
--- a/src/task-manager.ts
+++ b/src/task-manager.ts
@@ -52,20 +52,48 @@ export class TaskManager {
     return true
   }
 
-  // TODO: implement — remove a task by id, return true if removed, false if not found
+  /** Remove a task by id. Returns true if removed, false if not found. */
   remove(id: string): boolean {
-    throw new Error("not implemented")
+    return this.tasks.delete(id)
   }
 
-  // TODO: implement — update title/description/priority of a task
-  // return true if updated, false if not found
+  /**
+   * Update the title, description or priority of a task.
+   * Only keys explicitly present in `changes` are applied.
+   * Returns 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 ("title" in changes && changes.title !== undefined) task.title = changes.title
+    if ("description" in changes) task.description = changes.description
+    if ("priority" in changes && 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
+  /**
+   * Return all tasks sorted by the given field.
+   * priority: high > medium > low. createdAt: oldest first.
+   * status: pending > in_progress > completed.
+   */
   sortBy(field: "priority" | "createdAt" | "status"): Task[] {
-    throw new Error("not implemented")
+    const priorityRank: Record<Priority, number> = { high: 0, medium: 1, low: 2 }
+    const statusRank: Record<Status, number> = { pending: 0, in_progress: 1, completed: 2 }
+
+    return Array.from(this.tasks.values()).sort((a, b) => {
+      let delta: number
+      switch (field) {
+        case "priority":
+          delta = priorityRank[a.priority] - priorityRank[b.priority]
+          break
+        case "status":
+          delta = statusRank[a.status] - statusRank[b.status]
+          break
+        case "createdAt":
+          delta = a.createdAt.getTime() - b.createdAt.getTime()
+          break
+      }
+      return delta !== 0 ? delta : Number(a.id) - Number(b.id)
+    })
   }
 }
diff --git a/src/validator.ts b/src/validator.ts
index 27bf385..0f03fb5 100644
--- a/src/validator.ts
+++ b/src/validator.ts
@@ -4,25 +4,20 @@
 
 /**
  * Returns true if the string is a valid email address.
- *
- * BUG: the regex does not allow subdomains (e.g. user@mail.example.com fails)
- * and rejects valid TLDs longer than 4 chars (e.g. .museum, .travel).
+ * Supports subdomains and TLDs of any length (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}$/.test(value)
+  return /^[^\s@]+@[^\s@.]+(\.[^\s@.]+)*\.[a-zA-Z]{2,}$/.test(value)
 }
 
 /**
  * Returns true if the string is a valid URL (http or https).
- *
- * BUG: rejects URLs with ports (e.g. http://localhost:3000)
+ * Ports are permitted (e.g. http://localhost:3000).
  */
 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
   }