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Description
The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary MathematicsThis book contains 320 unconventional problems in algebra, arithmetic, elementary number theory, and trigonometry. Most of the problems first appeared in competitive examinations sponsored by the School Mathematical Society of the Moscow State University and the Mathematical Olympiads held in Moscow. Although most of the problems presuppose only high school mathematics, they are not easy; some are of uncommon difficulty and will challenge the
This book contains 320 unconventional problems in algebra, arithmetic, elementary number theory, and trigonometry. Most of the problems first appeared in competitive examinations sponsored by the School Mathematical Society of the Moscow State University and the Mathematical Olympiads held in Moscow. Although most of the problems presuppose only high school mathematics, they are not easy; some are of uncommon difficulty and will challenge the ingenuity of any research mathematician. Nevertheless, many are well within the reach of motivated high school students and even advanced seventh and eighth graders.The problems are grouped into twelve separate sections. Among these are: the divisibility of integers, equations having integer solutions, evaluating sums and products, miscellaneous algebraic problems, the algebra of polynomials, complex numbers, problems of number theory, distinctive inequalities, difference sequences and sums, and more.
Complete solutions to all problems are given; in many cases, alternate solutions are detailed from different points of view. Solutions to more advanced problems are given in considerable detail. Moreover, when advanced concepts are employed, they are discussed in the section preceding the problems. Useful in a variety of ways in high school and college curriculums, this challenging volume will be of particular interest to teachers dealing with gifted and advanced classes.
Binding Type: Paperback
Publisher: Dover Publications
Published: 09/28/1993
ISBN: 9780486277097
Pages: 480
Weight: 1.03lbs
Size: 8.76h x 5.16w x 0.90d
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★★★★★ 5
Great toy
Nice as a chew toy, fetch toy or for tug. My dogs liked it immediately. I love that it is not immediately destroyed, like most fabric toys.
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Reviewed in the United States on April 24, 2026
★★★★★ 5
Great for puppy gnawing!
I bought this toy a few months back and now I'm chiming in.. WOW! This is the FIRST toy our husky, Billie Eyelash, has NOT destroyed. She's about 16 Mos. and let no toy live this far except this one lol. I am amazed at the durability of this lil stick. When she needs to gnaw this thing is great! Gets right into the back teeth. They're is barely a mark on it and it's bouncy when you throw it. Yeah she loves it! 5 star
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Reviewed in the United States on May 5, 2026
★★★★★ 5
We LOVE these!!
Hands down the BEST dog toy we've found!! I have two pitbulls that are aggressive chewers and players.. we've had these about a month and they play with them everyday. Ordered two..still have two! They don't even have teeth marks in them. The durability is like nothing I've seen before. We've done name brand boxes specifically for bully breeds that are rather expensive, bought name brand toys that are also expensive..all broken or destroyed in a matter of a day, if that. For the price these are totally worth it! We'll be buying more down the road! I think these might actually last all summer!
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Reviewed in the United States on May 2, 2026
★★★★★ 5
This is a great ball for high energy dogs.
Color: Blue
I have a Belgian Malinois, so you can imagine the Maligator jaws. Just opened this today and let her play with it indoors. She LOVES IT. It wore her out and it’s a toy she can really stay focused on without needing me to throw or roll for her. It moves on its own! I supervised her play. I was hoping it was too big to get under the couch, but no. It goes right under it. I had to block off the gap so I didn’t have to keep getting it out from under for her. The outter “shell” is very durable! When she had resting moments, she chewed it pretty good - I could hear the material squeaking against her teeth. I was worried she was tearing it up, but nope! Not a mark on it. It’s easy to set up and operate. It needed charging before play. After hours of play, she was able to somehow unscrew the outter shell. This concerned me bc the smaller, inner ball mechanism came out but I saw it right away and was able to put it back together. So, make sure it’s screwed together tightly (which I thought I had done without breaking it) and check it from time to time to make sure it hasn’t loosened. This is a great ball for her incredible high energy drive. It gives her the work and fun play she needs to get tired, which I love. This toy is on the expensive end, but so far it’s worth it. Now we’ll see how long it lasts!
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Reviewed in the United States on October 7, 2025
★★★★★ 5
Love love it
Color: Blue
Best dog toy ever. I have a 1 year old boxer who is full of energy (understatement). This ball has provided more entertainment for us both than any dog toy I’ve ever purchased. Charge holds well and has a very resilient shell. I love it. Worth the price.
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Reviewed in the United States on May 23, 2026