A cross-figure (also variously called cross number puzzle or figure logic) is a puzzle similar to a crossword in structure, but with entries that consist of numbers rather than words, where individual digits are entered in the blank cells. The numbers can be clued in various ways: The clue can make it possible to find the number required directly, by using general knowledge (e.g. "Date of the Battle of Hastings") or arithmetic (e.g. "27 times 79") or other mathematical facts (e.g. "Seventh prime number") The clue may require arithmetic to be applied to another answer or answers (e.g. "25 across times 3" or "9 down minus 3 across") The clue may indicate possible answers but make it impossible to give the correct one without using crosslights (e.g. "A prime number") One answer may be related to another in a non-determinate way (e.g. "A multiple of 24 down" or "5 across with its digits rearranged") Some entries may either not be clued at all, or refer to another clue (e.g. 7 down may be clued as "See 13 down" if 13 down reads "7 down plus 5") Entries may be grouped together for clueing purposes, e.g. "1 across, 12 across, and 17 across together contain all the digits except 0" Some cross-figures use an algebraic type of clue, with various letters taking unknown values (e.g. "A - 2B, where neither A nor B is known in advance) Another special type of puzzle uses a real-world situation such as a family outing and base most clues on this (e.g. "Time taken to travel from Ayville to Beetown") Cross-figures that use mostly the first type of clue may be used for educational purposes, but most enthusiasts would agree that this clue type should be used rarely, if at all. Without this type a cross-figure may superficially seem to be impossible to solve, since no answer can apparently be filled in until another has first been found, which without the first type of clue appears impossible. However, if a different approach is adopted where, instead of trying to find complete answers (as would be done for a crossword) one gradually narrows down the possibilities for individual cells (or, in some cases, whole answers) then the problem becomes tractable. For example, if 12 across and 7 down both have three digits and the clue for 12 across is "7 down times 2", one can work