Connect Four

Connect Four (You = Red)

Your turn

Othello(Reversi)

Reversi / Othello (Player = Black)

Your turn

Macala(Kalah) played against the computer

Dots and Boxes - Learn by playing

Dots & Boxes

Grid: 3×3 boxes 4×4 boxes 5×5 boxes 6×6 boxes

Player 1's turn

Player 1: 0

Player 2: 0

How to play

1. Click an edge to draw it.
2. If you complete a box, it becomes yours and you go again.
3. Highest score wins.

Math table practice

 

🎲 Fun Multiplication Tables!

Choose a number to start practicing!

BrainVita / Marbles Solitaire Game

  BrainVita / Marbles Solitaire Game

<p>After reviewing the states of the game I am thinking of reachability.. whether starting from initial state is it possible to reach a given state and can you reach any configuration given the same starting state.. also predict number of and position of remaining marbles in the end

  What you are discovering is a deep property of peg solitaire / Brainvita: the game is not just about “making moves,” but about the structure of the state space.

Several important mathematical ideas arise naturally:

---

# 1. Reachability

Your question is:

> Starting from the standard initial state, can every board configuration be reached?

The answer is **no**.

Most conceivable configurations are actually impossible to reach.

The legal moves preserve hidden invariants, so the board is partitioned into “reachable” and “unreachable” regions.

This is why some positions may *look* close to a solution but are mathematically doomed.

---

# 2. State Space Graph

You can think of the game as a graph:

* each board configuration = a node

* each legal jump = an edge

Then solving the puzzle means:

> Find a path from the initial node to a final node.

The full graph is enormous, but highly constrained.

For the standard English cross board:

* total possible binary fillings ≈ (2^{33})

* but only a tiny fraction are reachable legally.

---

# 3. Position Classes (Very Important)

Peg solitaire has something called **position class theory**.

The board squares can be colored or labeled in modular patterns.

A move always changes these labels in constrained ways.

Therefore:

* some parity combinations can never occur

* some ending holes are impossible from certain starts

This is one reason why:

> Starting with center empty allows a 1-peg finish at center,

> but many other starts do not.

---

# 4. Predicting Final Marble Count

This becomes a conservation-law problem.

Each move:

* removes exactly 1 peg

* changes local geometry

If you start with:

[

N_0

]

pegs,

after (k) moves:

[

N = N_0 - k

]

So the parity of the number of pegs changes predictably.

But more interestingly:

## Geometry matters more than count

Examples of “dead” structures:

* isolated pegs

* edge traps

* disconnected clusters

* parity-locked regions

A configuration with 5 pegs may already be impossible to reduce further.

---

# 5. Can You Reach Any Configuration?

No.

This is equivalent to asking:

> Is the state graph connected?

It is not.

The graph breaks into disconnected components.

Some states:

* cannot be reached from the start

* cannot reach the goal

* can only appear in reverse play

---

# 6. Reverse Game Insight

A powerful method is:

## Play backwards

Instead of reducing pegs:

* start from final 1-peg state

* reverse jumps

* “grow” configurations

This reveals:

* which states are ancestors of a solution

* whether your current state lies in the solvable basin

This is how many optimal solvers work.

---

# 7. Computational Perspective

What you are thinking about is closely related to:

* graph search

* SAT solving

* combinatorics

* group invariants

* symbolic AI

* constraint propagation

A solver typically uses:

* BFS/DFS

* memoization

* symmetry reduction

* canonical board encoding

* transposition tables

---

# 8. The Deep Insight

You are moving from:

> “How do I solve this board?”

to:

> “What states are even theoretically possible?”

That is a transition from gameplay to mathematical structure.

This is exactly how research-level thinking begins in puzzles and algorithms.

---

# 9. One Famous Result

For the standard English board:

* Not every finishing hole is possible.

* Starting with center empty, ending at center is solvable.

* Some start/end combinations are provably impossible.

This can be shown using parity and pagoda functions.

---

# 10. Pagoda Functions (Advanced)

A pagoda function assigns weights to board positions.

A legal move can never increase total weight.

Therefore:

* if target state has larger weight than current state,

* it is unreachable.

This is a beautiful proof technique in peg solitaire theory.

---

You are very close to several computer science and mathematics topics:

* reachability analysis

* invariant theory

* game graph topology

* reversible computation

* search complexity

* combinatorial optimization

And Brainvita is actually an excellent laboratory for all of them.

Brainvita / Peg Solitaire

Click a marble, then click an empty hole two steps away in a straight line to jump.

Game to Guess Your Number(1-100)

Guess Your Number

Think of a number (1–100)

Remember it, don't tell me! Then press OK.

Does your number exist here?

I guessed your number!

Circular D3.js Sunburst chart with bugs solved and new bugs introduced by GPT

         

Yearly, Monthly and Weekly Charts with drill down with bugs solved and new bugs introduced by GPT

         

Circular D3.js Sunburst Chart created by GPT

         

Yearly, Monthly and Weekly Charts with drill down

         

Normed Space and Banach spaces

 Another curiosity arousal question here..

This one made me think "Shristi se pehle sat nahi tha" at 6.40 or 400 seconds.

Anyways This was exactly what I wanted to know about city block distances.

I was scared of the Hilbert Space and Curve until I saw this Video

I now have some fodder for my thoughts and a few more programs lined up to draw these types of space filling curves.

An idea that I was toying with struck now more deeply than earlier.

Suppose I have a polyhedral, say a dodecahedron.. How can I traverse it so that all points are visited?

Suppose it is a n-dimensional polyhedral, then?

3D Cube using Threejs in a HTML5 canvas-3D program