19
I have a solution with
Step by step:
14
I would suggest an alternate (simpler) strategy:
10
The player who can win is
by this strategy:
9
I think the answer for $14 \times 14$ is
Achieved as follows
While the best I've achieved for $9 \times 9$ is
Achieved as follows
8
Edit: my answer was inadequate. Only downvotes now please.
@Oray asked to follow up his answer and I found a fault in my previous work, resulting in
My original and obsolete answer was
8
First player wins
Example:
6
Here is an attempt which needs
wazirs:
5
For $14$x$14$ I got...
With this ...
Or with this...
4
A perhaps more elegant way to do
than @Glorfindel's solution is:
3
There are three necessary assumptions here:
(1) It is possible to build a physical mechanism that neither one of them can break.
If this were not the case, the only way trades could be made is by one person directly giving an item to the other. However, just giving items back and forth doesn't work: as soon as there's an imbalance in the wealth gained, ...
3
The pirate and the merchant could meet in a large, open field, stand about 10 paces apart, and face each other, the pirate facing southeast and the merchant facing northwest. Their vessels would need to be moored or parked in the direction to their rear. Here is an example graphic:
On cue, the pirate would walk due South 10 paces while the merchant would ...
3
Let's name the lines.
+---+---+
| K |
+---+ L + J +
| H I |
+ G +---+---+
| |
+---+---+ F +
| D E |
+ C + A +---+
| B |
+---+---+
The winner can be found by analyzing the game regardless of the position.
Now that we know the winner, who is which color?
And Bob's last move would ...
3
My solution:
Proof:
1) The optimal strategy is to...
2) If both are playing optimal...
3)
Bonus:
3
This answer will be updated as the series develops
One of the major factors that will heavily affect your solving experience is that it is difficult to visualise the moving parts. For your convenience I've made a tool that can create, visualise and simulate Square Spin puzzles. You can download it on GitHub
Now the question is "how should you solve them?". ...
3
I assume
Then one solution would be
As shown below
And
No idea if this is minimal though
3
A) If the board were instead very large (many billions of cells, for example), what limit could we place on the maximum sign density?
B) Again on a very large board, what limit could we place on the sign density if we eliminate the 4th rule and allow older signs to be blocked?
C) Solutions for odd-size boards, with and without rule 4
3
I have found a better answer than this answer by just playing with it:
with
not sure this is optimal though, but most likely. gonna write a program if noone does that until I wrote :D
2
Answer:
This of course assumes I happen to have a good calculator on me.
2
There is no strategy that is guaranteed to ever win, thanks to the BOOM rule.
If Alice picks $N = a^{124}\times b$, with $a$ and $b$ distinct primes, then $N$ has 250 factors. Bob's challenge is to determine $a$ and $b$.
The problem is that if he determines the order of the factors before determing both $a$ and $b$, then the BOOM rule can prevent him from ...
1
Find a narrow ravine and have one person stand on either side with the goods to be traded. Suspend a log over the ravine from a single rope in the center, so that it can spin freely and one end can be reached by either party. To start, each end of the log is firmly fixed to the ground on either side, so neither party can spin the log until both release it. ...
1
They could:
Before each deal:
1
Second player wins.
After that,
Then,
On first player's second turn,
In the end,
Alternately,
1
Solution in
plies:
Remark: the alternative try
isn't allowed because
Only top voted, non community-wiki answers of a minimum length are eligible
