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Honsberger R. — From Erdös to Kiev: Problems of Olympiad Caliber
Honsberger R. — From Erdös to Kiev: Problems of Olympiad Caliber

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Название: From Erdös to Kiev: Problems of Olympiad Caliber

Автор: Honsberger R.

Аннотация:

Ross Honsberger's love of mathematics comes through very clearly in From Erdös to Kiev. He presents intriguing, stimulating problems that can be solved with elementary mathematical techniques. It will give pleasure to motivated students and their teachers, but it will also appeal to anyone who enjoys a mathematical challenge. Most of the problems in the collection have appeared on national or international Olympiads or other contests. Thus, they are quite challenging (with solutions that are all the more rewarding). The solutions use straightforward arguments from elementary mathematics (often not very technical arguments) with only the occasional foray into sophisticated or advanced ideas. Anyone familiar with elementary mathematics can appreciate a large part of the book. The problems included in this collection are taken from geometry, number theory, probability, and combinatorics. Solutions to the problems are included.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 267

Добавлена в каталог: 04.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
A 100-coloring of the integers      127
A 1987$\times$1987 matrix      5
A certain product of sines      75
A challenging triangle construction      109
A colored 5$\times$41 array      104
A complicated inequality from Russia      239
A cube and a checkerboard      3
A game on divisors of an integer      11
A geometrical multiple choice problem      141
A Japanese temple problem on touching circles      223
A kind of Pythagorean triple      119
A property of a certain two intersecting circles      123
A property of a triangle having an angle of 30°      199
A property of integers around a circle      244
A property of pedal triangles      235
A property of sets {2, 5, 13, d}      74
A property of three concurrent circles      49
A property of two internally tangent circles      73
A sequence ${a_{n}}$ in which $2^{k}|a_{n}$ iff $2^{k}|n$      79
A special kind of palindrome      173
A subset of {1, 2,..., 3000} not containing both k and 2k      177
An algebraic multiple choice problem      143
An average over permutations      77
An awakward calculation      22
An Erdos problem on a companion sequence of integers      214
An Erdos problem on infinite subsequences      213
An inequality involving logarithms      151
An infinite sequence ${b_{i}$ with $(b_{m}, b_{n})$ a constant      51
An integral sequence beginning 1, 9, 8, 2      103
Arithmetic progressions in an 5$\times$5 array      93
Average number of runs in an integer      29
Average of the products of certain nonempty subsets of integers      167
Binary sequences of length 7      87
Black and white balls in an urn      1
Decomposing a square      13
Equations whose roots are given by their coefficients      159
Integers with digits {1, 2, 3, 4, 5}      48
Isosceles-triangle decompositions of a triangle      14
Longest string of consecutive integers adding to $3^{11}$      19
Monochromatic triangles on 7 points in space      217
Numbering triangles in a triangulated polygon      133
On $\sum x_{i}x_{j}, x_{s}, x_{t}=\pm 1$      71
On 2 triangles with a common circumcenter      56
On 2-colorings of a circle      171
On 44 integers$\leq$125      72
On a bubble sort      21
On a certain 10-element subset      55
On a certain infinite decimal: rational or irrational?      72
On a certain irrational distances and triangles of rational area      191
On a certain sum of disjoint intervals that add to 1988      59
On a certain triangulation of a triangle      145
On a cyclic and an inscriptible property of a quadrilateral      63
On a factor of $ax^{17}+bx^{16}+1$      96
On a hexagon of tangents to the incircle of a triangle      183
On a partition of the integers      10
On a quadrilateral and triangle of equal area in a circle      192
On a series of freight trains      89
On a square around the incircle of a triangle      67
On an average unsigned distance = 1/2      8
On an nth-degree function with f(2)$\geq3^{n}$      6
On constructing a certain chord in a circle      147
On floors and ceilings      187
On foreign languages      229
On interior segments in a certain polyhedron      95
On isosceles right angled pedal triangles      153
On minimizing a certain segment in a triangle      43
On perfect squares in arithmetic progressions      197
On reflecting a triangle in each of its sides      137
On the Gergonne triangle of a triangle      99
On the integer parts of certain square roots      221
On the locus of a certain centroid in space      209
On the perpendicularity of certain segments in a triangle      230
On the power-sum of an integer      135
On the product of 5 consecutive integers      207
On the roots of $x^{n+2}-2x+1=0$      115
On the sequence ${S_{b}/b}$      241
On the sequence ${[n\sqrt{2}]}$      107
On triangles $P_{i}, P_{j}, P_{k}$ containing a given point Q      131
Opening a safe      83
Probability of 5 withdrawals forming certain arithmetic progressions      37
Sequences from the alphabet {a, b, c}      164
Solving $5^{x}\cdot 7^{y}+4=3^{z}$ in nonnegative integers      211
Some 3 of every subset of 4 planar points form a triangle      45
The least upper bound of a certain sequence      33
The only minimum value of a certain integral sum $S_{n}$      25
The power mean inequality      249
The sequence $n, \tau(n), \tau(\tau(n))$      41
Trisecting a series of binomial coefficients      203
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