out that (i) the last digit of 12 across must be even, (ii) the first digit of 7 down must be 1, 2, 3 or 4, and (iii) the first digit of 12 across must be between 2 and 9 inclusive. (It is an implicit rule of cross-figures that numbers cannot start with 0; however, some puzzles explicitly allow this) By continuing to apply this sort of argument, a solution can eventually be found. Another implicit rule of cross-figures is that no two answers should be the same (in cross-figures allowing numbers to start with 0, 0123 and 123 may be considered different.) A curious feature of cross-figures is that it makes perfect sense for the setter of a puzzle to try to solve it themself. Indeed, the setter should ideally do this (without direct reference to the answer) as it is essentially the only way to find out if the puzzle has a single unique solution. Alternatively, there are computer programs available that can be used for this purpose; however, they may not make it clear how difficult the puzzle is. Given that some basic mathematical knowledge is needed to solve cross-figures, they are much less popular than crosswords. As a result, very few books of them have ever been published. Dell Magazines publishes a magazine called Math & Logic Problems four times a year that includes these puzzles, which they name "Figure Logics"; the eighteen puzzles contained within each issue generally increase in difficulty, from easy to "challenger". A magazine called Figure it Out, which was dedicated to number puzzles, included some, but it was very short-lived. This also explains why cross-figures have fewer established conventions than crosswords (especially cryptic crosswords). One exception is the use of the semicolon (;) to attach two strings of numbers together, for example 1234;5678 becomes 12345678. Some cross-figures voluntarily ignore this option and other "non-mathematical" approaches (e.g. palindromic numbers and repunits) where same result can be achieved through algebraic means. External links "Cross-figure Puzzles by Yochanan Dvir" "On Crossnumber Puzzles and The Lucas-Bonaccio Farm 1998" The Little Pigley Farm crossnumber puzzle and its history by Joel Pomerantz Cross-figure/Crossword Hybrids by Jordan Inman Cross Figures for Android Logic puzzles Recreational mathematics