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Nov
4
comment The number of bottles of beer one can buy with $10, after exchanging bottles and caps
Borrow a bottle cap from a friend, use it and your three saved bottle caps to buy a beer, and drink it, and return the bottle cap you just got to your friend. You can then use the two empty bottles you have to buy another beer, ending up with 17. And after this, borrow an empty beer bottle from a friend ...
Oct
14
awarded  Yearling
Jun
18
answered Calculation of Shannon entropy given the mutual information of Binary strings
Jun
17
comment Calculation of Shannon entropy given the mutual information of Binary strings
-1: The mutual information can be 0 and the entropy of C can be $H(1/4)\cdot l$ if you let A and B be independent strings where each bit is 0 or 1 with probability $1/2$. And by altering this example slightly, you can make the mutual information $1/2$ and not change $H(C )$ much. This upper bound is wrong.
Jun
13
comment Calculation of Shannon entropy given the mutual information of Binary strings
First, is the mutual information 1/2 or $\ell/2$? (If you're copying this question from somewhere, note that 1/2 and $l/2$ can look very similar.) Second, I think your guess is wrong; try some examples.
Apr
30
comment Probability of random card from deck
Are there any jokers in the deck?
Apr
22
comment Show $ex \leq e^x$ for all $x \in \mathbb{R}$
You've already made one mistake: $e - e^x$ is not always less than 0.
Apr
11
answered Example of pairwise independent random process with expected max load $\sqrt{n}$.
Feb
9
comment Integer Linear Programming
You want $x_3$ to be as big as possible, and $x_1$ to be as small as possible. Use the greedy method to find $x_3, x_2,$ and $x_1$ satisfying the equations with these criteria (not necessarily integer). Now find the best integer solution. Think about the values of the variables mod 3.
Oct
27
comment Mathematician vs. Computer: A Game
@pew: Isn't 30 the best choice for 31 as well? It ties with 5 and 7 for 32, but for 33 and above, the best choice seems to be prime.
Oct
14
awarded  Yearling
Sep
30
awarded  Good Answer
Aug
4
comment $q|2^p -1 \Longrightarrow p |q-1$ for primes $p,q$?
Hint for first statement: use an elementary theorem from group theory.
Aug
4
comment Distributing half a deck of cards
This seems like an ideal problem on which to use the inclusion-exclusion formula.
Jul
1
comment Number of unique permutations of a 3x3x3 cube
Any arrangement can be rotated to yield 24 superficially different arrangements. You can put any of the six faces on the bottom, and then with that face on the bottom, o can rotate it to have any of four faces facing south.
May
18
answered Should I understand a theorem's proof before using the theorem?
Apr
8
awarded  Nice Answer
Mar
30
comment A confusion about RP class of problems
If the answer is incorrect, the machine will never accept. Thus, if the machine accepts, the answer is correct. It's the logical contrapositive.
Oct
14
awarded  Yearling
Oct
4
comment Why are certain greek characters used predominantly for certain purposes in mathematics?
@DonAntonio: my comment is meant to point out that this should really be treated as two separate questions: (a) why are Greek letters used in mathematics? and (b) why do certain letters get used predominantly for certain purposes?