Ed Pegg
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 Nov 23 comment Is there a field size such that it makes perpetual “candy crush” Running infinitely isn't likely. Even with only two colors, there is always a chance of a checkerboard grid dropping down. Getting a count of the 2-color rectangular boards with no 3-in-a-row would be a good first step. Nov 21 comment Is there a convex polygon such that it cannot be tiled with some number of congruent connected pieces? Could prove it's not dissectable into quadrilateral Q. Start by looking at angles A&J, which do not sum to Pi. Q must fit into angle A. That introduces two new acute angles to fill. If Q has parallel sides, J can't be filled. Otherwise, the bottom edge can't be covered. Nov 17 revised Graph with maximal number of faces added 373 characters in body Nov 17 answered Graph with maximal number of faces Nov 17 comment Why find triangles in graphs? One example -- a complex connection of gears. If there is a triangle, or any odd circuit, the network of gears will fail. As a social network test, if there are no triangles in a large social network, it is unbelievable. Nov 16 revised Which cubic graphs have an eigenvalue of $\sqrt{6}$? added 148 characters in body Nov 16 answered Which cubic graphs have an eigenvalue of $\sqrt{6}$? Nov 16 answered Is there a convex polygon such that it cannot be tiled with some number of congruent connected pieces? Nov 16 revised Queen moves — The Squared Chain Puzzle deleted 1 character in body Nov 16 revised Queen moves — The Squared Chain Puzzle Added the claimed solution for 10 moves. Nov 16 comment Proof that a secant line intersects a circle in exactly two points (according to Hilbert's axiomatic system) Start with the definition of a secant line. Nov 12 revised Minimal diagonal intersections in a convex polygon Improved the 9 point solution. Nov 11 revised Minimal diagonal intersections in a convex polygon added 198 characters in body Nov 11 comment Minimal diagonal intersections in a convex polygon They haven't gotten very far with A230281, have they? Ten points is not the regular decagon. Not sure how they got a(9) might be 94. Nov 11 asked Minimal diagonal intersections in a convex polygon Nov 10 comment Breaking a stick to form a triangle Switch the problem around -- what is the probability for n pieces? Nov 10 comment Breaking a stick to form a triangle Suppose the stick randomly breaks into $n$ pieces of length 1, 2, 4, 8, 16, 32, ...? I don't think you can get "always" out of this. Also, computing the probability is subject to the same problems as the Random Chord Paradox. Nov 10 asked Queen moves — The Squared Chain Puzzle Nov 9 answered Covering eleven dots in the plane with eleven coins - counterexample? Nov 3 accepted Fractional oblongs in unit square via the Paulhus packing technique