xkcd

Thank you (n^2)/d(n!) is equal to pi(n) when n goes to infinity (where pi(n) is the counting function of primes) Is there any interpretation of this "equality"? My last post because I wanted to point out to this. Good luck and good bye! To the moderator : No one asked me about clarificatio...

Post closed.
Good bye and good luck!
I`m not welcomed so bother?

22!=1124000727777607680000
The number 22! is a 22 digit number

11240
00727
77760
76800
00

Find a number n such as n! is n^2 digit number

More generally find n such as n! is n^k digit number (k>2)

Can we build an algorithm showing quickly that a configuration has or has not solution? I mean without giving that solution.
Test of puzzle`s solvability if you wish.

If no one has a solution I will post mine in the next days.

This puzzle could be a 2 player game Nim-like. A print and play game using pencils and a printed board. The grid 9x9 or 3nx3n start empty. On his turn a player choose three vertices to form a DISTINCT isosceles triangle and put on each circle his symbol (* versus x for example). Player alternate. Th...

The right to progress is to ask for clarity before trying to solve the puzzle. So good luck! It is a hard puzzle. Jaap you are right for the first comment. My examples were not giving triangles other than right. I answered quickly because I had in mind many pictures I did not post. I assumed that pe...

samples.gif In this picture you have 3 different shapes. You could list more than those 3. Each color represent a shape. Draw a grid 9x9 with intersections instead of circles and try to imagine all kind of isosceles triangles linking 3 vertex. After doing that try place the maximal number of distin...

I will add there there are many shapes that you could as long as they use isosceles triangles. The circles are just a representation of points. You could reduce them to points if you want so then you will see all the possible distinct shapes. Good luck! It is hard puzzle harder than you could imagine.

Read what was written in the picture : "At right you have samples of isosceles triangles connecting three circles" Is there any precision about right triangle or not? no. So triangles could be right or not. Just watch carefully my examples : you have right triangles and not right triangles...

It is obvious that each triangle remove only 3 circles. Otherwise it will be simple.
Why I showed three colors for each triangle?
So you have theoretically 81/3=27 as maximal number of shapes. But the reachable maximal number is far less.
Your solution is not correct.

2 goals :
- connect all the 81 circles
- use the maximal number of distinct isosceles triangle shapes
The board of 81 circles is at left waiting for you to fill it.

Good luck!

Players move by swapping their stones (their color versus the opponent`s color).
The main hurdle is to avoid cycles.

This is the 2 game player at the set up.

I've had another realization. Take a look at this configuration of pieces (M is male, F is female, O is offspring, and x is an opponent's piece of some kind): M x x x O O x F O x O F x O O x M x x If you are forced to make two paths, one of the offspring has to be excluded. However, if you are allo...

Here is the solution of my first puzzle 8x8 given in my first post :

Here is the solution the puzzle 4x4 with the configuration
AABB
AABB
CCDD
CCDD

This configuration 4x4
AABB
AABB
CCDD
CCDD

has a solution

Until now I did not find 4x4 without solution.
Maybe someone could help by giving a 4x4 without solution

This configuration 8x8

AAAABBBB
AAAABBBB
AAAABBBB
AAAABBBB
CCCCDDDD
CCCCDDDD
CCCCDDDD
CCCCDDDD

has not solution

There is a way to solve this 8x8 in particular. If you break the board 8x8 into 4 boards 4x4 you will find easily the solution. It is not a general method to find at least one solution. I still think that there is some method or algorithm to solve any 8x8 board quickly. I will post the solution if n...

For this game it must be played in a board 2nx2n to avoid giving a slight advantage to the blue player. As we talk about families and fertility an idea came to my mind : introducing neutral pieces ("orphans"). So any player could make path using them and as possible consequence disrupting ...

In board 4x4 once we find one solution we could generate 2^8 solutions minus 1 (255 solutions) by switching the colors. We assume that the links (straight lines)remain as they are. So there is a way (messy for sure) to compute at least (in terms of percentage) the number of solutions out of 4^16. To...

What are invariants no matter the board size : - 4 colors (blue, red, yellow, green) - 4 lengths (1,r(2),r(5),r(10). Easy to compute the number needed. Number of straight lines used is equal. In case 4x4 thi number is equal to 2. In case 8x8, this number is equal to 8. - linking all the circles 2 by...

Ah ok. Now I understand what you were talking about. Intersections between the links (straight lines) does not matter at all. What is important is that all circles be connected by pairs : one straight line linking 2 circles. Player must use 8 straight lines of each length. 8*2*4=64 circles. Now we n...

You wrote : "Are the rules just straight lines only between different colors..." That is the first rule : straight line between 2 different colors. That means that it is not allowed to link circles having the same color. " and the number of intersections each line has? It looks like t...

Here are the 2 boards with circles. I replaced the colors by letters (4 colors 4 letters the choice was arbitrary so B is not blue for example) As you can see the links then there is no problem. Good luck! A B C C D A D C A B A B D C B D D C B D B D C A A C A D C A D C C D B A D B A B B D C D A C C ...

I can do it for you if it just come to the colors inside the circles (It will take me 30 minutes) but how could I replace the links (in yellow) between circles? After rethinking I believe that it will hard to guess the rules. So if no one find the rules (which is part of the puzzle) then I will post...

This is a new kind of puzzle
You have only one picture and you need to decrypt it to solve.
No comment about the rules. It is up to you to guess them

Good luck!

It is up to the player to optimize his score by making the best choice under the constraints of the rules. A player could use only one pair if he is able to connect all his off-springs. No player is forced to use all his 3 pairs. Sometimes even the choice of the order of counting is important. Assum...

The statement is correct. I could not write it with this wonderful clarity. In the counting process a player must indicate the path from a chosen male (or female) to chosen female (or male) by removing the off-springs. So an off-spring can not be used twice. He belongs to one family not two or more....

This new game is based on the idea of fertility. Each player has 3 kind of pieces : - males (3) - females (3) - off-springs (the number will depend on the size of the board) Each player has pieces of the same color (blue versus red for example) Hex Board : 11x11 Blue (or red) has then 3 males, 3 fem...