TOUGHNESS REQUIREMENTS FOR STEELS: AN INTERNATIONAL COMPENDIUM

By AMELIA THOMAS

CONTENTS INTRODUCTION THE INTERNATIONAL MATHEMATICAL OLYMPIAD THE IMO COMPENDIUM BASIC CONCEPTS AND FACTS ALGEBRA POLYNOMIALS RECURRENCE RELATIONS INEQUALITIES GROUPS AND FIELDS ANALYSIS GEOMETRY TRIANGLE GEOMETRY VECTORS IN GEOMETRY BARYCENTERS QUADRILATERALS CIRCLE GEOMETRY INVERSION GEOMETRIC INEQUALITIES TRIGONOMETRY FORMULAS IN GEOMETRY NUMBER THEORY DIVISIBILITY AND CONGRUENCES EXPONENTIAL CONGRUENCES QUADRATIC DIOPHANTINE EQUATIONS FAREY SEQUENCES COMBINATORICS COUNTING OF OBJECTS GRAPH THEORY PROBLEMS IMO 1959 CONTEST PROBLEMS IMO 1960 IMO 1961 IMO 1962 IMO 1963 IMO 1964 IMO 1965 IMO 1966 SOME LONGLISTED PROBLEMS 1959–1966 IMO 1967 LONGLISTED PROBLEMS 3 10 IMO 1968 3 10 1 CONTEST PROBLEMS 3 10 2 SHORTLISTED PROBLEMS 3 11 IMO 1969 3 11 1 CONTEST PROBLEMS 3 11 2 LONGLISTED PROBLEMS 3 12 IMO 1970 3 12 1 CONTEST PROBLEMS 3 12 2 LONGLISTED PROBLEMS 3 12 3 SHORTLISTED PROBLEMS 3 13 IMO 1971 3 13 1 CONTEST PROBLEMS 3 13 2 LONGLISTED PROBLEMS 3 13 3 SHORTLISTED PROBLEMS 3 14 IMO 1972 3 14 1 CONTEST PROBLEMS 3 14 2 LONGLISTED PROBLEMS 3 14 3 SHORTLISTED PROBLEMS 3 15 IMO 1973 3 15 1 CONTEST PROBLEMS 3 15 2 SHORTLISTED PROBLEMS 3 16 IMO 1974 3 16 1 CONTEST PROBLEMS 3 16 2 LONGLISTED PROBLEMS 3 16 3 SHORTLISTED PROBLEMS 3 17 IMO 1975 3 17 1 CONTEST PROBLEMS 3 17 2 SHORTLISTED PROBLEMS 3 18 IMO 1976 3 18 1 CONTEST PROBLEMS 3 18 2 LONGLISTED PROBLEMS 3 18 3 SHORTLISTED PROBLEMS 3 19 IMO 1977 3 19 1 CONTEST PROBLEMS 3 19 2 LONGLISTED PROBLEMS 3 19 3 SHORTLISTED PROBLEMS 3 20 IMO 1978 3 20 1 CONTEST PROBLEMS 3 20 2 LONGLISTED PROBLEMS 3 20 3 SHORTLISTED PROBLEMS 3 21 IMO 1979 3 21 1 CONTEST PROBLEMS 3 21 2 LONGLISTED PROBLEMS 3 21 3 SHORTLISTED PROBLEMS 3 22 IMO 1981 3 22 1 CONTEST PROBLEMS 3 22 2 SHORTLISTED PROBLEMS 3 23 IMO 1982 3 23 1 CONTEST PROBLEMS 3 23 2 LONGLISTED PROBLEMS 3 23 3 SHORTLISTED PROBLEMS 3 24 IMO 1983 3 24 1 CONTEST PROBLEMS 3 24 2 LONGLISTED PROBLEMS 3 24 3 SHORTLISTED PROBLEMS 3 25 IMO 1984 3 25 1 CONTEST PROBLEMS 3 25 2 LONGLISTED PROBLEMS 3 25 3 SHORTLISTED PROBLEMS 3 26 IMO 1985 3 26 1 CONTEST PROBLEMS 3 26 2 LONGLISTED PROBLEMS 3 26 3 SHORTLISTED PROBLEMS 3 27 IMO 1986 3 27 1 CONTEST PROBLEMS 3 27 2 LONGLISTED PROBLEMS 3 27 3 SHORTLISTED PROBLEMS 3 28 IMO 1987 3 28 1 CONTEST PROBLEMS 3 28 2 LONGLISTED PROBLEMS 3 28 3 SHORTLISTED PROBLEMS 3 29 IMO 1988 3 29 1 CONTEST PROBLEMS 3 29 2 LONGLISTED PROBLEMS 3 29 3 SHORTLISTED PROBLEMS 3 30 IMO 1989 3 30 1 CONTEST PROBLEMS 3 30 2 LONGLISTED PROBLEMS 3 30 3 SHORTLISTED PROBLEMS 3 31 IMO 1990 3 31 1 CONTEST PROBLEMS 3 31 2 SHORTLISTED PROBLEMS 3 32 IMO 1991 3 32 1 CONTEST PROBLEMS 3 32 2 SHORTLISTED PROBLEMS 3 33 IMO 1992 3 33 1 CONTEST PROBLEMS 3 33 2 LONGLISTED PROBLEMS 3 33 3 SHORTLISTED PROBLEMS 3 34 IMO 1993 3 34 1 CONTEST PROBLEMS 3 34 2 SHORTLISTED PROBLEMS 3 35 IMO 1994 3 35 1 CONTEST PROBLEMS 3 35 2 SHORTLISTED PROBLEMS 3 36 IMO 1995 3 36 1 CONTEST PROBLEMS 3 36 2 SHORTLISTED PROBLEMS 3 37 IMO 1996 3 37 1 CONTEST PROBLEMS 3 37 2 SHORTLISTED PROBLEMS 3 38 IMO 1997 3 38 1 CONTEST PROBLEMS 3 38 2 SHORTLISTED PROBLEMS 3 39 IMO 1998 3 39 1 CONTEST PROBLEMS 3 39 2 SHORTLISTED PROBLEMS 3 40 IMO 1999 3 40 1 CONTEST PROBLEMS 3 40 2 SHORTLISTED PROBLEMS 3 41 IMO 2000 3 41 1 CONTEST PROBLEMS 3 41 2 SHORTLISTED PROBLEMS 3 42 IMO 2001 3 42 1 CONTEST PROBLEMS 3 42 2 SHORTLISTED PROBLEMS 3 43 IMO 2002 3 43 1 CONTEST PROBLEMS 3 43 2 SHORTLISTED PROBLEMS 3 44 IMO 2003 3 44 1 CONTEST PROBLEMS 3 44 2 SHORTLISTED PROBLEMS 3 45 IMO 2004 3 45 1 CONTEST PROBLEMS 3 45 2 SHORTLISTED PROBLEMS SOLUTIONS CONTEST PROBLEMS 1959 CONTEST PROBLEMS 1960 CONTEST PROBLEMS 1961 CONTEST PROBLEMS 1962 CONTEST PROBLEMS 1963 CONTEST PROBLEMS 1964 CONTEST PROBLEMS 1965 CONTEST PROBLEMS 1966 LONGLISTED PROBLEMS 1967 4 10 SHORTLISTED PROBLEMS 1968 4 11 CONTEST PROBLEMS 1969 4 12 SHORTLISTED PROBLEMS 1970 4 13 SHORTLISTED PROBLEMS 1971 4 14 SHORTLISTED PROBLEMS 1972 4 15 SHORTLISTED PROBLEMS 1973 4 16 SHORTLISTED PROBLEMS 1974 4 17 SHORTLISTED PROBLEMS 1975 4 18 SHORTLISTED PROBLEMS 1976 4 19 LONGLISTED PROBLEMS 1977 4 20 SHORTLISTED PROBLEMS 1978 4 21 SHORTLISTED PROBLEMS 1979 4 22 SHORTLISTED PROBLEMS 1981 4 23 SHORTLISTED PROBLEMS 1982 4 24 SHORTLISTED PROBLEMS 1983 4 25 SHORTLISTED PROBLEMS 1984 4 26 SHORTLISTED PROBLEMS 1985 4 27 SHORTLISTED PROBLEMS 1986 4 28 SHORTLISTED PROBLEMS 1987 4 29 SHORTLISTED PROBLEMS 1988 4 30 SHORTLISTED PROBLEMS 1989 4 31 SHORTLISTED PROBLEMS 1990 4 32 SHORTLISTED PROBLEMS 1991 4 33 SHORTLISTED PROBLEMS 1992 4 34 SHORTLISTED PROBLEMS 1993 4 35 SHORTLISTED PROBLEMS 1994 4 36 SHORTLISTED PROBLEMS 1995 4 37 SHORTLISTED PROBLEMS 1996 4 38 SHORTLISTED PROBLEMS 1997 4 39 SHORTLISTED PROBLEMS 1998 4 40 SHORTLISTED PROBLEMS 1999 4 41 SHORTLISTED PROBLEMS 2000 4 42 SHORTLISTED PROBLEMS 2001 4 43 SHORTLISTED PROBLEMS 2002 4 44 SHORTLISTED PROBLEMS 2003 4 45 SHORTLISTED PROBLEMS 2004 REFERENCES