From Erdos to Kiev: Problems of olympiad caliber by Ross Honsberger

By Ross Honsberger

Ross Honsberger's love of arithmetic comes via very basically in From Erdös to Kiev. He offers exciting, stimulating difficulties that may be solved with common mathematical strategies. it's going to supply excitement to prompted scholars and their lecturers, however it also will attract someone who enjoys a mathematical problem. lots of the difficulties within the assortment have seemed on nationwide or overseas Olympiads or different contests. hence, they're rather tough (with ideas which are all of the extra rewarding). The ideas use straight forward arguments from ordinary arithmetic (often now not very technical arguments) with merely the occasional foray into subtle or complicated principles. a person conversant in undemanding arithmetic can delight in a wide a part of the booklet. the issues incorporated during this assortment are taken from geometry, quantity concept, chance, and combinatorics. suggestions to the issues are incorporated.

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37. 8. 3 1 + 16 12 1 + 40 4 + 15 3 1 1 1 + + + 16 8 3 4 1 1 1 22. + + 14 15 6 11 5 5 24. + + 36 72 6 39. 41. 43. 45. 47. 9 3 14 42 5 8 9 24 7 9 13 1 2 1 32. 16 32 8 8 9 12 1 3 5 3 34. 3 + 5 2 + 4 2 4 8 4 3 3 36. 8 - 5 3 8 4 3 7 3 3 38. 5 + 2 8 - 3 16 16 8 4 3 7 1 7 40. 8 - 4 7 - 4 16 8 4 16 4 8 5 17 42. 4 3 + 9 + 6 5 9 12 20 9 7 1 2 7 7 44. 5 + 3 3 + 4 + 3 + 4 16 12 6 5 10 15 5 9 7 1 1 1 46. 12 16 - 4 - 2 - 3 + 2 8 12 2 16 6 4 Find the perimeter of the triangular plot in Illustration 1. 30. 712!

29. A large rectangular tank is to be made of sheet metal as follows: 3 ft by 5 ft for the top and the base, two sides consisting of 2 ft by 3 ft, and two sides consisting of 2 ft by 5 ft. Find the volume of this container. 30. Suppose an oil pan has the rectangular dimensions 14 in. by 16 in. by 4 in. Find its volume. 31. Find the weight of a cement floor that is 15 ft by 12 ft by 2 ft if 1 ft3 of cement weighs 193 lb. 32. A trailer 5 ft by 6 ft by 5 ft is filled with coal. Given that 1 ft3 of coal weighs 40 lb and 1 ton ϭ 2000 lb, how many tons of coal are in the trailer?

14 16 15 18 20 25 54 72 112 144 7 28 12 21. 16 12 24. 36 112 27. 128 18. 30. 525 1155 Copyright 2009 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. 7 Change each fraction to a mixed number in simplest form: 31. 78 5 21 3 57 37. 6 70 40. 2 16 34. 32. 11 4 33. 45 36 84 38. 9 67 16 15 39. 5 12 35. 7 28 3 36. ■ Addition and Subtraction of Fractions 33 Change each mixed number to an improper fraction: 5 6 2 44. 5 3 7 47. 6 8 5 50. 12 6 41.

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