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 Mar 15 comment In how many of the integer numbers between 0 and 10,000 does the digit 3 appear to the left of 4 Minor: you could avoid materializing the list at all, e.g. sum('3' in l and '4' in l[l.index("3"):] for l in map(str, range(10001))). Sep 24 awarded Autobiographer Feb 7 comment How to choose between an odd number of options with a fair coin It's worth noting that the "flip the coin once for each option" approach has a major advantage: it will work even if the coin is unfair, because each option has the same chance to be accepted or rejected at each round. It can be pretty inefficient, of course. Aug 9 comment Given three integers in $\{0,\ldots,100\}$ which sum up to $100$. What is the probabilty that two of them are the same? Isn't 3*51 153? (FWIW, a brute force calculation I just did gave 153/5151.) May 13 awarded Caucus Oct 20 comment Probability of getting at least 1 white ball If you apply your argument to the case of drawing three balls, each of which is blue, you'd get $95/72$.. Aug 19 comment Is there any way to determine the first $3$ digits of $2^m-2^n$ ($n\leq m\leq 10^{100}$) @MichaelAnderson: as I said, you need as many digits as you need to ensure that the interval of possible values is tight enough. Since I'm lazy, I wouldn't even bother working out how many I'd need beforehand: I'd simply do the computation at some low precision, see whether or not the interval confirms the first few digits, and if not, repeat at higher precision. But this is very much a brute force approach, and there's probably a slick base-2 related one instead. Aug 19 comment Is there any way to determine the first $3$ digits of $2^m-2^n$ ($n\leq m\leq 10^{100}$) @MichaelAnderson: a good arbitrary precision library won't have any problems with these numbers at all. 2^(10^100) ~ 2.551789e+3010299956639811952137388947244930267681898814621085413104274611271081‌​892744245094869272521181861720. You don't need to store every digit, only enough that the interval is tight enough to confirm the first few digits. Jun 17 comment What is $i^{i^{\,{}^{.\,^{.\,^{.\,^i}}}}}$ equal to? This question seems on the same subject. Apr 3 comment I have learned that 1/0 is infinity, why isn't it minus infinity? @Cor_Blimey: no, the limit of $4/x$ as $x\to2$ is $2$, it doesn't approach $2$. $2$ is the limit because it's the number which is approached. Apr 3 comment I have learned that 1/0 is infinity, why isn't it minus infinity? @JackManey: why the scare quotes around learnt? It's unusual in American English, but more common elsewhere. Jan 31 comment Why is $m$ used to denote slope? ‘We designate the slope of a line by m because the word slope starts with the letter m; I know of no better reason.' Jan 30 comment password lock problem What if the password were 100? When would it open? Jan 29 awarded Commentator Jan 29 comment Which of the numbers $99^{100}$ and $100^{99}$ is the larger one? @cardinal: I should explain why @nightcracker's Python returns False. Python allows chained comparisons (1 <= x < 9), so it was interpreting 99**100 > 100**99 == True as one of these. True has an integer comparison value of 1, so this is really 99**100 > 10**99 == 1, which is false. 99**100 > 100**99 and (99**100 > 10**99) == True both return True as you'd expect. Jan 21 comment Finding how many terms of the harmonic series must be summed to exceed x? See oeis.org/A002387 for some information. Jan 16 comment truth table equivalency Hint: if you went to the store and it rained, then if someone says that either you didn't go to the store or it didn't rain, they'd be lying, wouldn't they? (This hint is for how to avoid an "and" by using "or" and "not" instead.) Jan 15 comment Calculating limits - difference of cubes That should be $3x^2+3 h x + h^2$, not $3x + 3 h + h^2$, no? Jan 2 comment Problems that are largely believed to be true, but are unresolved @EricNaslund: depends where you grew up, I think. "Able to be solved" is usually the second definition in most dictionaries, and I've myself heard people in the UK and Canada use "soluble group". Dec 30 comment The number is a perfect square if and only if $k=n$ @r.e.s.: 729 is a typo for 792. k=3,n=792 gives 95725884816, which is 309396^2.