tailieunhanh - .The Contest Problem Book VAmerican High School Mathematics Examinations and American Invitational

.The Contest Problem Book V American High School Mathematics Examinations and American Invitational Mathematics Examinations 198S1988 Problems and solutions compiled and augmented by George Berzsenyi Rose-Hulman Institute of Technology Stephen B Maurer Swarthmore College THE MATHEMATICAL ASSOCIATION OF AMERICA .NEW MATHEMATICAL LIBRARY published by The Mathematical Association of America Editorial Committee Underwood Dudley, Editor DePauw University Ross Honsberger, University of Waterloo Daniel Kennedy, Baylor School Michael J. McAsey, Bradley University Mark E. Saul, Bronxville Schools Peter Ungar Anneli Lax, Consulting Editor New York University The New Mathematical Library (NML) was begun in 1961 by the School Mathematics Study Group to make available to high school students short expository. | THE CONTEST J PROBLEM BOOK V AMERICAN HIGH SCHOOL MATHEMATICS EXAMINATIONS AHSME AMERICAN INVITATIONAL MATHEMATICS EXAMINATIONS AIME 19831988 Problems and solutions complied and augmented by GEORGE BERZSENYI and STEPHEN B MAURER A cube of cheese c xy x I 0Sxy xắ 1 is cut along the planes X y y t and X X How many pieces are there A 5 B 6 C 7 D 8 E 9 . 27. 1987 AHSME It is possible to place positive integers into the twenty-one vacant squares of the 5x5 square shown on the right so that the numbers in each row and column form arithmetic sequences. Find the number that must occupy the vacant square marked by the asterisk . 6. 1988 A1ME 74 186 103 0 The Mathematical Association of America New Mathematical Library The Contest Problem Book V American High School Mathematics Examinations and American Invitational Mathematics Examinations 1983-1988 Problems and solutions compiled and augmented by George Berzsenyi Rose-Hulman Institute of Technology Stephen B Maurer Swarthmore College 38 THE MATHEMATICAL ASSOCIATION OF AMERICA NEW MATHEMATICAL LIBRARY published by The Mathematical Association of America Editorial Committee Underwood Dudley Editor DePauw University Ross Honsberger University of Waterloo Daniel Kennedy Baylor School Michael J. McAsey Bradley University Mark E. Saul Bronxville Schools Peter Ungar Anneli Lax Consulting Editor Aiew York University The New Mathematical Library NML was begun in 1961 by the School Mathematics Study Group to make available to high school students short expository books on various topics not usually covered in the high school syllabus. In three decades the NML has matured into a steadily growing series of over thirty titles of interest not only to the originally intended audience but to college students and teachers at all levels. Previously published by Random House and L. W. Singer the NML became a publication series of the Mathematical Association of America MAA in 1975. Under the auspices of the MAA the NML will continue to grow