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..10c8833 100644
--- a/src/date-utils.ts
+++ b/src/date-utils.ts
@@ -6,15 +6,15 @@
  * 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.
+ * Day counts are rounded on the magnitude of the difference so that past and
+ * future dates the same distance away report the same number of days.
  */
 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) {
@@ -25,7 +25,7 @@ export function formatRelative(date: Date, now: Date = new Date()): string {
     const h = Math.round(Math.abs(diffHours))
     return diffMs > 0 ? `${h} hour${h !== 1 ? "s" : ""} ago` : `in ${h} hour${h !== 1 ? "s" : ""}`
   }
-  const d = Math.abs(diffDays)
+  const d = diffDays
   return diffMs > 0 ? `${d} day${d !== 1 ? "s" : ""} ago` : `in ${d} day${d !== 1 ? "s" : ""}`
 }
 
diff --git a/src/string-utils.ts b/src/string-utils.ts
index 63fba18..8d07b85 100644
--- a/src/string-utils.ts
+++ b/src/string-utils.ts
@@ -11,10 +11,20 @@ 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.
+/**
+ * Truncate to at most maxLength characters, cutting at a word boundary.
+ * The trailing ellipsis counts toward maxLength, so the result may be shorter.
+ */
 export function truncate(str: string, maxLength: number): string {
-  throw new Error("not implemented")
+  if (str.length <= maxLength) return str
+
+  const ellipsis = "..."
+  if (maxLength <= ellipsis.length) return str.slice(0, maxLength)
+
+  const cut = str.slice(0, maxLength - ellipsis.length)
+  const lastSpace = cut.lastIndexOf(" ")
+  const body = lastSpace > 0 ? cut.slice(0, lastSpace) : cut
+  return body + ellipsis
 }
 
 export function slugify(str: string): string {
@@ -24,8 +34,7 @@ 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.trim().split(/\s+/).length
 }
diff --git a/src/task-manager.ts b/src/task-manager.ts
index a920e85..12f4df6 100644
--- a/src/task-manager.ts
+++ b/src/task-manager.ts
@@ -17,6 +17,18 @@ export interface Task {
 }
 
 export class TaskManager {
+  private static readonly priorityRank: Record<Priority, number> = {
+    high: 0,
+    medium: 1,
+    low: 2,
+  }
+
+  private static readonly statusRank: Record<Status, number> = {
+    pending: 0,
+    in_progress: 1,
+    completed: 2,
+  }
+
   private tasks: Map<string, Task> = new Map()
   private nextId = 1
 
@@ -52,20 +64,36 @@ 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")
+    return this.tasks.delete(id)
   }
 
-  // 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
+  /**
+   * Returns a sorted copy of the tasks. Priority orders high > medium > low,
+   * status follows the lifecycle order, and createdAt returns oldest first.
+   */
   sortBy(field: "priority" | "createdAt" | "status"): Task[] {
-    throw new Error("not implemented")
+    const tasks = Array.from(this.tasks.values())
+    switch (field) {
+      case "priority":
+        return tasks.sort(
+          (a, b) => TaskManager.priorityRank[a.priority] - TaskManager.priorityRank[b.priority],
+        )
+      case "createdAt":
+        return tasks.sort((a, b) => a.createdAt.getTime() - b.createdAt.getTime())
+      case "status":
+        return tasks.sort(
+          (a, b) => TaskManager.statusRank[a.status] - TaskManager.statusRank[b.status],
+        )
+    }
   }
 }
diff --git a/src/validator.ts b/src/validator.ts
index 27bf385..5441531 100644
--- a/src/validator.ts
+++ b/src/validator.ts
@@ -3,26 +3,24 @@
  */
 
 /**
- * Returns true if the string is a valid email address.
+ * Returns true if the string looks like 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).
+ * This is a format check only, not a deliverability or security guarantee.
  */
 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)
 }
 
 /**
- * Returns true if the string is a valid URL (http or https).
+ * Returns true if the string is a valid URL (http or https). Ports are allowed.
  *
- * BUG: rejects URLs with ports (e.g. http://localhost:3000)
+ * This is a format check only. It is not an SSRF guard — callers that pass the
+ * value to a server-side request must apply their own host allow-list.
  */
 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
   }