Part 1 . Discrete Problems Problems and Results in Combinatorial Geometry °

I have published during my very long life many papers with similar titles . In this note, I report on progress made on some of the old problems and discuss also some new ones, and I repeat some old problems which seem to have been forgotten by everybody (sometimes including myself) . First, a very incomplete list is given of some papers dealing with these and related questions . I have published three survey papers on this subject [1-3] . I want to call attention to the excellent book of Hadwiger and Debrunner which originally appeared in German and French . This book was translated by Klee who also added much original material and brought the book up-to-date (up to about 1964) [4] . This book contains a great deal of interesting material and can be used as a textbook to learn the subject, but contains few unsolved problems . (Unfortunately, it is out of print .) A very fruitful source of problems and results is the much expanded 1981 edition of W. Moser's collection, "Research Problems in Discrete Geometry" (McGill University) . The nucleus of this collection was the old problems of the late Leo Moser . In Elemente der Mathematik there is a section entitled "Ungelőste Probleme" which was edited by Hadwiger and in the American Mathematical Monthly there is a similar section edited by Guy ; both often contain geometrical problems . See also the papers by Fejes-Toth, Grünbaum, and Klee that are quoted in [1] . G. Purdy and I plan to write a book on various problems in combinatorial geometry . We hope the book will appear in this decade .