SKU: 81758478319

AoPS Intermediate Counting & Probability Text and Solution Set

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Description

AoPS Intermediate Counting & Probability Text and Solution SetDavid Patrick Paperback Text: 400 pages. Solutions: 208 pages. An intermediate textbook in counting and probability for students in grades 9 12, containing topics such as inclusion exclusion, recursion, conditional probability, generating functions, graph theory, and more. Overview Continue your exploration of more advanced counting and probability topics from former USA Mathematical Olympiad winner David Patrick. This book is the follow up to the

David Patrick
Paperback
Text: 400 pages. Solutions: 208 pages.
An intermediate textbook in counting and probability for students in grades 9-12, containing topics such as inclusion-exclusion, recursion, conditional probability, generating functions, graph theory, and more.

Overview

Continue your exploration of more advanced counting and probability topics from former USA Mathematical Olympiad winner David Patrick. This book is the follow-up to the acclaimed Introduction to Counting & Probability textbook.

Topics covered in this book include inclusion-exclusion, 1-1 correspondences, the Pigeonhole Principle, constructive expectation, Fibonacci and Catalan numbers, recursion, conditional probability, generating functions, graph theory, and much more.

As with all of the books in Art of Problem Solving's Introduction and Intermediate series, the text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, so the student has a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which counting and probability techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains over 650 problems. The solutions manual contains full solutions to all of the problems, not just answers.

Text ISBN: 978-1-934124-06-2
Solutions ISBN: 978-1-934124-07-9

Table of Content

Sample Pages

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SKU: 81758478319

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Verified Purchase
Isidro mora
Grantham, US
★★★★★ 5
Very durable.
Style: Snake
My frenchie loves this snake very durable
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on June 13, 2026
J
jj
Natrona Heights, US
★★★★★ 4
A bit wider than I expected
Style: Coyote
I thought this was going to be a "flat" toy but was a bit surprised to see that it was more of a 3D shape than flat. It's unfortunately a bit too wide for my small/medium sized terrier so he really only grabs and chews on the tail and ears. It is pretty durable though and has held up well.
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on April 20, 2026
B
Brande B
Lowell, US
★★★★★ 5
Toughest dog toy we've ever owned! Jasper approved!
Style: Elk, Style: Elk
If you are the owner of a "power chewer" who usually turns standard plushies into a snowstorm of stuffing in under five minutes, the HOUND2O Elk Stuffed Animal is the heavy-duty solution you’ve been looking for. This isn't just a toy; it’s a rugged piece of outdoor-grade gear that manages to stay "plush" while being nearly indestructible. Here is why this elk is the gold standard for aggressive chewers. The "Ballistic" Build The secret to its toughness lies in the materials. Unlike cheap fleece or thin polyester, the HOUND2O Elk is engineered for extreme durability. Ballistic Nylon Shell: The body is wrapped in high-denier ballistic nylon—the same type of material used in tactical gear. It’s incredibly resistant to punctures and tears from sharp canine teeth. Reinforced TPR Accents: The "antlers" and specific high-wear points are reinforced with Thermoplastic Rubber (TPR). This gives your dog a satisfying, grippy texture to gnaw on without compromising the toy’s structural integrity. Extreme Stitching: The seams are double-stitched and recessed, making it nearly impossible for a dog to find a "weak spot" to start a rip. Built for Adventure: This toy is marketed for "outdoor adventures," and it truly lives up to that branding: Water-Resistant & Buoyant: Unlike most stuffed animals that become soggy, heavy sponges, this elk is water-resistant and it floats. It’s the perfect companion for a trip to the lake or a game of fetch in the pool. Easy to Clean: Because the material is so dense, mud and slobber don't soak in deeply. A quick rinse with a hose or a wipe-down with soap and water makes it look brand new after a day in the dirt. High Visibility: The vibrant colors and distinct shape make it easy to spot in tall grass or murky water, so you won't lose it during a long-range game of fetch. Engaging (But Tough) Squeaker For many aggressive chewers, the goal is to "silence" the squeaker as fast as possible. Protected Internal Squeaker: The squeaker is buried deep within the ballistic layers, making it much harder for a dog to pinpoint and puncture. It provides that high-value auditory feedback that keeps dogs engaged without being an easy "kill point" for the toy. Performance at a Glance Durability - Ballistic nylon and TPR are a "power chewer" dream. Versatility - Floats, easy to clean, and works indoors/outdoors. Engagement - Mixed textures (nylon + rubber) keep dogs interested. Value - Outlasts 10 standard plush toys combined. The HOUND2O Elk is a 10/10 for any pet parent tired of throwing away shredded toys. It is incredibly tough, intelligently designed, and built to withstand the "ruffest" play. While no toy is truly 100% indestructible for every single dog, this is as close as a plush-style toy can possibly get. If your dog loves the "thrill of the hunt," try hiding this elk in some tall grass or bushes outside. Its tough shell can handle the brush, and it’s a great way to provide mental stimulation alongside a heavy chewing session!
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Reviewed in the United States on March 13, 2026
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Verified Purchase
Melissa Withers
Bozeman, US
★★★★★ 2
Not as durable as it looks
Style: Snake
Our half pittbull and half american bulldog tore this apart in 5min.
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Reviewed in the United States on April 27, 2026
A
Amazon Customer
Draper, US
★★★★★ 5
Good looking toy that has held up well
Style: Coyote, Style: Coyote
Very durable toy that our little dog especially loves. It's the perfect size for a small dog and she doesn't destroy toys anyway so it's been great. It does feel very durable though and would take our chewer a little while to get to it as well. I'm not sure it looks like a coyote but the dogs don't seem to mind. It's an attractive toy that looks great and is constructed well so it's not like a slobbery mess when left out. Good value for the money and would make a great gift because it looks higher quality than most toys.
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Reviewed in the United States on April 14, 2026

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