The tradition of arithmetical puzzles. An attempt of reconstruction

The survey is devoted to the history of “arithmetical riddle problems” found in Diophantus’ Arithmetica, Anthologia Palatina, ancient Chinese Nine chapters of the mathematical art, The Book of Abacus of Fibonacci, Medieval Armenian “Questions and solutions”, some Arabian and Indian sources, etc. Many well-known “arithmetical riddle problems” known from our school textbooks were invented a long time ago - in Hellenistic antiquity, if not earlier. As a rule, their solving was based on techniques of oral arguments and account, which are restored in this paper.