Combinatorics question about choosing non consecutive integers
How many ways can $r$ nonconsecutive integers be chosen from the first $n$ integers?
What effect does serial downvoting have on my rep cap? So I was the victim of serial downvoting the other day, and just had it automagically reversed. Rather than simply removing the previous votes, I was given a bonus lump of rep with the reason "serial downvote reversal". The downvotes and the bonus show up on different days. Since a whole day's quota worth of downvotes equates to quite a fraction of my daily rep cap, what happens in the following circumstances?   I get 200+ rep on a particular day, but I am serial downvoted (later reversed) back to under 200. Does this day count as reaching cap? I get 200+ rep the next day, and I am also credited back the rep. Is the rep bonus immune to the rep cap in the same way bounties are? On the day I get my rep bonus, it is enough to take me to 200 rep. Does this count as capping? 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Keep values selected after form submission Analyzing $\biggl\lfloor{\frac{x}{5}}\bigg\rfloor=\bigg\lfloor{\frac{x}{7}}\bigg\rfloor$ How many non negative integral values of $x$ satisfy the equation :$$\biggl\lfloor{\dfrac{x}{5}}\bigg\rfloor=\bigg\lfloor{\dfrac{x}{7}}\bigg\rfloor$$.   My try:  Writing few numbers and putting in the required equation.  $\underbrace{0,1,2,3,4}_{\implies 0=0},\underbrace{5,6}_{\displaystyle\times},\underbrace{7,8,9}_{\implies 1=1},\underbrace{10,11,12,13}_{\displaystyle\times} ,\underbrace{14}_{\implies 2=2},\underbrace{15,16,17,18,19,20}_{\text{LHS gives 3 but RHS gives 2}},\underbrace{21,22,23,24}_{\text{LHS gives 4 but RHS gives 3}}$.  The point which I wish to make here is that after $14$ we'll get $5's$ multiple before than $7's$, hence $\forall x \geq 15 \implies \biggl\lfloor{\dfrac{x}{5}}\bigg\rfloor&gt;\bigg\lfloor{\dfrac{x}{7}}\bigg\rfloor$  Hence the only solution are: $\{0,1,2,3,4,7,8,9,14\}$. Does these make sense?  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Here is what happens:  $ sudo visudo &gt;&gt;&gt; /etc/sudoers: syntax error near line 28 &lt;&lt;&lt; sudo: parse error in /etc/sudoers near line 28 sudo: no valid sudoers sources found, quitting Where do I find system sounds? After installing gm-notify I see the option of hearing a sound every time a new e-mail arrives in my Gmail inbox, but I don't know where Ubuntu (10.4) stores the system sounds to assign one. Any ideas? Thanks.