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 Oct 4 comment Two question on Permutation and Combination @ Debanjan: I think your list is the list of possible teams, not the list of possible matches (M1,W1)v(M2,W2), (M1,W2)v(M2,W1). Oct 4 comment What is the minimal coloring of a planar graph with swaps? Are you interested in all planer graphs with vertices of degree 4, or just the square grid type graph? Sep 27 answered Find thickness of a coin Sep 27 comment Cutting sticks puzzle I am also confused by your suggestion that the number of solutions for the hardest combination is increasing. The link that Chandru1 posted contains a table of the number of solutions for the "hardest" combination. Note that for any even n there is a starting position which has only one solution (up to initial stick reordering and reordering of segments within each initial stick). This is the starting position where there are n/2 sticks of length n+1. Sep 27 comment Cutting sticks puzzle I like the idea of solving using OEIS :-) You haven't explained what you are counting as a "solution" above. For example when n=3 there are two possible starting positions: (3,3) and (6). Depending on how you are counting solutions there is either 1 solution {1,2,3} (unordered), or maybe solutions should be counted by where each end stick came from - e.g. (3,3) has a solution where you break 2 off the first stick, and another solution where you break 1 off the second stick, etc. Sep 22 comment Connected simple cubic graph +1 Very clean :-) The final inequality should be the other way around: $n \leq 4$. Sep 16 comment Grid of overlapping squares Sorry - I have just noticed that I've labelled the grid starting from (1,1) instead of (0,0) as in your question. I've left this as it is because it makes the maths slightly simpler. Sep 16 answered Grid of overlapping squares Sep 10 awarded Supporter Sep 8 awarded Teacher Sep 8 answered Terminology for handling probabilities with partial knowledge