Index to Mathematical Problems 1980-1984



To determine which journals and contests have been indexed, see the list on the inside back cover. A more detailed list can be found in the Journal Issue Checklist (page 421). That section also tells you which columns in these journals were indexed.


Given a topic that you are interested in, consult the Subject Classification Scheme (page 7) to find the classification closest to your topic of interest. Then go to the page number listed for that topic and scan the problems looking for those of interest to you. A quick overview of the classification scheme can be found in the Table of Contents.


You can look in the Keyword Index (page 501) under various keywords that pertain to your topic of interest to locate specific problems associated with this keyword. This is particularly useful when you remember a memorable word or phrase from the problem you are searching for. You can also check the Title Index (page 373) to see if the keyword appears in the title of a problem.


If you know the author of a problem (or are interested in problems by a specific author), use the Author Index (page 335). For references to biographical information about problemists, see page 487.


Given a problem number (for example, one obtained from the Keyword Index), in order to locate the text of the problem, use the Problem Locator (page 15) to find the page in this index where the text of the problem is printed. Scanning around on that page may also show you related problems that may be of interest to you.

Note that the text for the problem as printed in this index may only be a summary of the full text as originally printed. We have omitted extraneous information and may have reworded the problem to make the notation consistent. To find the original complete wording for this problem, consult the Problem Chronology (page 299) to find the journal, volume, and page number where the problem was proposed.

If the problem does not appear in the Problem Locator, this means that the text of the problem does not appear in this index (because the problem was not published during the years 1980–1984). Consult the Problem Chronology (page 299) to find a reference to a solution or comment concerning this problem.

To find problems of a certain type or difficulty level, determine which journals or contests normally publish problems of the kind that you are interested in. Then scan the appropriate portion of the subject index for problems from these journals.


Once you find a specific problem that interests you, go to the Problem Chronology (page 299) and look up this problem number. You will then find references to where the problem was published (journal, volume, issue, and page number) as well as references to all published solutions, partial solutions, and comments related to this problem. Additional references may be found in the Citation Index (page 479), which lists journal articles that reference problems covered by this index.


Consult the Citation Index (page 479) to find references to specific contest problems. Articles about complete contests (frequently reprinting the problems from the contest and often containing solutions) can be located in the Contest References section of the Citation Index (page 486).


The list of abbreviations for the journal names can be found on the inside back cover of this index. A more complete list of journal abbreviations is given on page 437. If you want to examine a problem or solution from some journal and that journal is not in your library, consult the Journal Information section (page 435) for data about the journal, such as the ISSN number. Your librarian should be able to help you locate a library that carries this journal from the bibliographic information given. The name of the publisher is also given, along with the address to write to for subscription information if the journal is still active.


For unfamiliar terms or notation, consult the Notation (page 3) or the Glossary (page 499).


A convenient compilation of those problems proposed during the years 1980–1984 that remain unsolved as of 1991 can be found on page 463. An author index to the proposers of these unsolved problems can be found on page 477. Consult the Problem Chronology (page 299) to locate references to partial solutions to these problems. Additional references to these problems in the literature can be found in the Citation Index (page 479).


A list of problem books that have been reviewed during the years 1980–1984 can be found on page 488.


References to journal articles appear in square brackets. See page 489 for the full bibliographic citation.


Each section of this index also includes additional details on how to use that section.


Use this section to locate problems related to one or more specific topics. It may be helpful to read the following summary description of how problems are sorted and classified before using this section.

Each problem in this book has been assigned a single classification of the form

major subject/secondary subject/tertiary subject/...

The length of this classification depends on the problem. Some problems have as few as two classes (only a major subject and secondary subject), while most have somewhere between three and eight classes assigned to them.

All secondary subjects, tertiary subjects, etc. are indexed in this section. Each entry is followed by a list of all classifications in which the entry appears. Each classification in the list is truncated at the position where the indexed entry begins. For example, “AL/inequalities [6]” (see abbreviation key below) appears under the entry “logarithms”. This means that six problems (some possibly duplicates) have been assigned the classification “Algebra/inequalities/logarithms” (possibly with additional subclasses following “logarithms”). Counts are omitted for classifications assigned to one problem only. For classifications in which the indexed entry is subordinate to the tertiary subject, only the major subject, secondary subject, and tertiary subjects are listed. Classifications for Alphametics problems are omitted.

In the Subject Index section (where the problem statements appear), major subjects appear alphabetically, secondary subjects appear alphabetically within each major subject, tertiary subjects appear (implicitly , in most cases) alphabetically within each secondary subject, and so on. Therefore it is relatively easy to locate problems directly from the Classification Index.

Abbreviation key:

AL = Algebra GA = Games ST = Set Theory
AN = Analysis HA = Higher Algebra SG = Solid Geometry
AM = Applied Mathematics LA = Linear Algebra S = Statistics
C = Combinatorics NT = Number Theory SL = Symbolic Logic
CR = Cryptarithms P = Probability T = Topology
G = Geometry RM = Recreational Mathematics TR = Trigonometry

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