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 Oct16 comment 100 sequential parking spaces I don't think we can ignore all the cars above k in your third sentence. For example in the case n=100 if the first car to park happens to be car 3 then we have a much higher chance of parking 3 cars in total than 2 (as cars don't have to park in their own space). Dec5 awarded Popular Question May14 awarded Caucus Mar18 comment What was the first bit of mathematics that made you realize that math is beautiful? (For children's book) @K.Stm. Ah ok! So |(a,b)| = 2 :-) Mar15 comment What was the first bit of mathematics that made you realize that math is beautiful? (For children's book) @K.Stm. The first point is that the size of any open interval is the same as the size of all the real numbers. This can be seen by stretching a function like tan to create a bijection between the two. You can read more here: en.wikipedia.org/wiki/Cardinality_of_the_continuum Sep10 comment Sequence Sum {1/2 + 1/4 + 1/6 +…} to infinite I think you want four eighths (and correspondingly four terms in the last bracket on the first line). Jul18 comment Divisibility of large number The problem here is the "..." bit. Although 3000, 1500 and 750 are even, and so allow you to use the difference of two squares, 375 is odd, and so there is no next step in this sequence. May24 awarded Student May24 comment What is the maximum number of edges in a planar bipartite graph which have partitions of order 7 and 15? @DanielPietrobon I thought the two halves of a bipartite graph were called partitions? I'm asking about a bipartite graph with 7 vertices in one half and 15 in the other. May24 awarded Editor May24 revised What is the maximum number of edges in a planar bipartite graph which have partitions of order 7 and 15? Minor edit for clarity - I'm not looking for something simpler than Euler Characteristic or 3 utilities problem. May24 asked What is the maximum number of edges in a planar bipartite graph which have partitions of order 7 and 15? Oct27 awarded Commentator Oct27 comment Why can't there be a monotone function with domain $\mathbb{R}$ and range $\mathbb{R} \setminus \mathbb{Q}$? Ah yes - I missed that the question was about hitting all irrationals. Very easy to visualise, thanks! :-) Oct26 comment Why can't there be a monotone function with domain $\mathbb{R}$ and range $\mathbb{R} \setminus \mathbb{Q}$? Just because the function is increasing, doesn't mean that it will reach 0, or 1. Also I don't think you can assume there is a real number y with f(y)=1 if you're also assuming f:R->R\Q. I'm sure you can fix both these issues by a linear transformation of your increasing function (e.g. all increasing functions are a linear transform of an increasing function that has both positive and negative values). Sep7 awarded Yearling Aug25 answered How many ways to form a committee, subject to certain restrictions? Aug23 comment Find thickness of a coin @Mechanical snail: The initial point of contact will almost certainly be one of the four 'corners' shown above. Consequently the centre of mass will almost certainly be to the left/right of the point of contact, and will cause the coin to fall on a head/tail/edge (at which point it will be above the point of contact). Oct5 answered What is the minimal coloring of a planar graph with swaps? Oct4 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).