13
votes
Accepted
frog on a number line
It's easy to see by transforming the problem into a symmetric one - instead of a 1/3 vs. 2/3 jump to B or D, make a third branch so it's a uniform 1/3 chance of going to B, D, or D' (which in turn has ...
- 3,991
9
votes
8
votes
frog on a number line
Let's make every state in the game worth an amount of money to be in:
A B C D E
$6 $4 $2 $1 $0
With the way that the prices are ...
- 1,395
7
votes
Was Humpty Dumpty right?
NOTE: Answer pre-dates correction to the question. Humpty Dumpty is now correct.
Humpty Dumpty is wrong.
Both twins tell the truth on Sunday, so neither of them could give that reply. Hence it is ...
- 246
5
votes
frog on a number line
The transition probability matrix is
$$
P =
\begin{pmatrix}
1& 0& 0& 0& 0\\
1/2& 0& 1/2& 0& 0\\
0&...
- 11.5k
4
votes
Accepted
Colliding Bullets again
I believe the exact answer you're looking for is
Explanation:
This appears to corroborate Dmitry's rather than dipodomys's simulation, even if Dmitry's is flawed in design. The conclusion is at ...
- 2,172
3
votes
Was Humpty Dumpty right?
Humpty Dumpty is wrong.
(well, depending on what assumptions you make interpreting the puzzle)
Humpty's answer assumes that this is equally likely to have occurred on any given day regardless of the ...
- 31
3
votes
Expected number of steps
Here are the first $10$ values, obtained via a Markov chain with $\binom{2N}{N}$ states, one for each placement of $N$ cars in $2N$ spots:
\begin{matrix}
N & \text{expected number} \\
\hline
1 &...
- 11.5k
2
votes
Colliding Bullets again
Update: fixed a mistake in my code where I didn't properly account for whether the trajectory of the bullets colliding was after the bullets were fired.
I took a shot at this problem by coding up a ...
- 121
1
vote
frog on a number line
Let $p$ be the probability that a frog standing on C ultimately reaches A, as required.
This probability $p$ will therefore apply both to a frog starting out its journey, and to a frog who has ...
1
vote
frog on a number line
This already has a solution but for the sake of variety, here's a numerical solution in Google Sheets (also applicable to Excel).
A
B
C
D
E
1
0
0
0
0
1
=1/2 * A1 + 1/2 * C1
=1/3 * B1 + 2/3 * D1
=1/...
- 269
1
vote
frog on a number line
Consider the set $S$ of all paths from $C$ to $A$, where a path is represented by a concatenation of $B$, $C$, and $D$ ending with $A$. For instance, $BCDCBA$ represents the path $C->B->C->D-&...
- 111
1
vote
Expected number of steps
Partial Answer - Simulation
Welcome to this site @12HackingEarth.
Those assumptions are made in the simulation (If I understood correctly your challenge):
Any car can be selected, independently of ...
- 669
Only top scored, non community-wiki answers of a minimum length are eligible