Peter Shor
Reputation
2,045
Top tag
Next privilege 2,500 Rep.
Create tag synonyms
 Apr 24 comment Dimension about space of matrices of order 3 over the field of the real. That's the basis of matrices with trace 0, but can all matrices with trace 0 can be expressed as $AB-BA$? Apr 15 comment Determining the favored penny on a chessboard But if you had 3 squares, and wanted to flip at most one penny, you could do it: make the favorite penny be the only one with H (or T). 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.