I found another math rendering plugin refered to here: http://www.illigal.uiuc.edu/web/kumara/2007/04/10/latex-math-plugin-for-wordpress/
It is based on LaTeX.
Note To Self: Kumara Sastry appears to be an interesting an talented person. He studies in the area of genetic algorithms. An idea I have is to study talented people and make a blog and the subsequently a company based around these people.
Easy LaTeX – author interesting blog to punch around also
Given a number if the sum of these digits is equal to a number that is divisible by 3 then the number is divisible by 3. Proof follows
Research Links
Consider the following set of dice.
The probability that A rolls a higher number than B, the probability that B rolls higher than C, and the probability that C rolls higher than A are all 5/9, so this set of dice is nontransitive. In fact, it has the even stronger property that, for each die in the set, there is another die that rolls a higher number than it more than half the time.
Now, consider the following game, which is played with a set of dice.
If this game is played with a transitive set of dice, it is either fair or biased in favor of the first player, because the first player can always find a die that will not be beaten by any other dice more than half the time. If it is played with the set of dice described above, however, the game is biased in favor of the second player, because the second player can always find a die that will beat the first player's die with probability 5/9. The following tables show all possible outcomes for all 3 pairs of dice.
|
Player 1 chooses die A Player 2 chooses die C |
Player 1 chooses die B Player 2 chooses die A |
Player 1 chooses die C Player 2 chooses die B |
|||||||||||
|
C \ A |
2 | 4 | 9 |
A / B |
1 | 6 | 8 |
B​ / C |
3 | 5 | 7 | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 3 | C | A | A | 2 | A | B | B | 1 | C | C | C | ||
| 5 | C | C | A | 4 | A | B | B | 6 | B | B | C | ||
| 7 | C | C | A | 9 | A | A | A | 8 | B | B | B | ||
We present a solution to round 1 question 5 from the 2019 New Zealand Mathematical Olympiad. This problem involves describing all values of a quartic expression which is a perfect square.