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 Jun20 comment Is there an example of nonassociative arithmetic addition? @JoshuaHonig What Martigan and mixedmath say is true but there are two other aspects : 1) in rings, fields and their generalizations (i.e. modules, near-ring, near-fields, k-, there are at least two binary operations, and by analogy with the classical situation, one operation is called addition and the other multiplication. 2) addition is typically associated with the idea of the magnitude of the result being close to the magnitude of the larger of the elements being combined and multiplication with expansion of magnitude (analogy to the area, the volume, a list of possibilities etc.) May5 comment Finding an equation of circle which passes through three points Are you sure that your solution covers all degenerate cases ? Feb10 comment Expressing a sequence with two sigma notation $\NN$ does have zero. You don't need to add it. Feb10 comment Circular permutations - $n$ sitting at a round table without repeating neighbors @0ana : 13524 and 14253 are not related by a rotation but by a reversal. Feb5 comment The discriminant of an integral binary quadratic form and the discriminant of a quadratic number field Is this something you came up by yourself ? If not, please give the source by respect of the authors. Dec12 comment zeros of Incomplet Gamma function @TylerHG : these are not zeroes but misinterpretations of underflows. Oct28 comment What does a non-mathematician need to google to learn more about latin squares in which each number in each row always has a different successor? @hcc23 : I am also interested by your opinion on my sequential solution to your experimental problem. Oct28 comment What does a non-mathematician need to google to learn more about latin squares in which each number in each row always has a different successor? No you don't miss anything. You spotted a mistake in my terminology. I should have said cyclic (I will edit it), because in the Williams construction described on the H. Bruin page, this is the same array of differences from one column to the next. In fact, this property might be considered a disadvantage if there is an interaction between the properties of your operations and this sequence of difference, making this series of experimental tests not "mixed" or "unbiased" enough. Oct27 comment What does a non-mathematician need to google to learn more about latin squares in which each number in each row always has a different successor? Dear @hcc23, you just require that the pairs do not repeat horizontally, am I right ? You also don't need to exclude circular pairs (seeing the latin square as a cylinder or a torus) ? Jan30 comment Proof concerning Latin squares You are welcome. Consider reading a book about problem solving. The one which was fashionable in my time was Polya's, but there a lot of resources available on the web and in libraries. Apr14 comment Orthogonal Latin Square 6*6 See my answer for a link on the original paper. A physical copy of the journal of the French "Association for l'Avancement des Sciences" is not so easy to find outside France (where most University libraries have it). May25 comment Non-associative, non-commutative binary operation with a identity what's the point of adding y if it is zero! Are you sure this was what you meant? May25 comment When $G'$/$G''$ and $G''$ both are cyclic groups @Basil R: you should edit your title and question. May24 comment A question about integral quadratic forms The left part of your equation is what mathematicians call a (integral) quadratic form. There is a lot of results about the integers n they can represent or not. May24 comment Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian thanks a lot for these references. We speak of Exponent semigroup, Levi semigroup, etc. What is the operation on these sets? May23 comment How to split an integral exactly in two parts @Byron: thanks for this careful explanation with references. May20 comment Probability of a point taken from a certain normal distribution will be greater than a point taken from another? Just to be sure: do you consider the two draws to be strictly independent, i.e. the mechanism simulated by the second draw is not modified or influenced by the value of the first? If this is the case, the problem can be rephrased very simply, while perhaps not realistic. Also note that there is Cross-Validated, the SE site for statistical Q&A. May20 comment Logic Puzzle of the age of three sons @Amy : see my answer to R. Israel. No this is not a standard, just a possible thought process of the problem's author. As these problems are supposed to make youngsters manipulate properties of integers, this made-up rule is a way to introduce the composite/prime distinction in the problem. May20 comment Logic Puzzle of the age of three sons @Robert Israel: I agree with you, and I should not have presented my interpretation as if I believed that buildings are somehow figurate numbers. Just a hint or a trick toward a possible solution. As user6312 said, we are not doing mathematics here. We are just trying to outguess/reverse engineer a very vague and inconsistent fantasy world which is more or less shared among variants of these kinds of problem. This riddle is only a support for successive hypothesis and manipulation of integers, not a scientific slice of reality. May19 comment Logic Puzzle of the age of three sons @svenkatr : You are right that this way was not listed. But if there is (one) older son, 1,6,6;13 is not possible.
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