Connect 4 is thought to be a solved sport.

After Connect 4 is Excellent, Connect 3 is Great being trivialised by @Trenin, I’m introducing the ultimate puzzle I needed to share to puzzling.SE 🙂

Connect X, a Connect 4 variant.

Both gamers play like join 4 and fill the grid i.e. they do not cease when 4 or extra of a shade is related in a row, as opposite to basic join 4. However, they will not precisely take flip like in join 4. Player 1 will play first one in every of its colours. Then, every participant performs two consecutive instances till the grid is crammed.

First flip
| … | … | … | … | … | … | … |
| … | … | … | … | … | … | … |
| … | … | … | … | … | … | … |
| … | … | … | … | … | … | … |
| … | … | … | … | … | … | … |
| … | … | … | O | … | … | … |

Second flip
| … | … | … | … | … | … | … |
| … | … | … | … | … | … | … |
| … | … | … | … | … | … | … |
| … | … | … | … | … | … | … |
| … | … | … | … | … | … | … |
| X | … | … | O | … | … | … |

Third flip
| … | … | … | … | … | … | … |
| … | … | … | … | … | … | … |
| … | … | … | … | … | … | … |
| … | … | … | … | … | … | … |
| X | … | … | … | … | … | … |
| X | … | … | O | … | … | … |

and many others. O performs for turns 4 and 5

This means of taking turns is fairer for participant 2 and is impressed from Tennis tiebreak sport.

If a participant does a join 7, the sport stops and he wins, in any other case, when the grid is crammed, the scoring system works as follows:

For every:

• Connect 2: $i$ factors
• Connect 3: $j$ factors
• Connect 4: $okay$ factors
• Connect 5: $l$ factors
• Connect 6: $m$ factors
• Connect 7: $+infty$ factors (the sport stops earlier and the participant who did it wins)

$(i,j,okay,l,m) in mathbb R_+^5:quad i<j<okay<l<m$

Here is an instance with:

$(i,j,okay,l,m) = (1,2,4,8,16)$

| X | O | X | X | O | O | X |
| X | O | O | X | O | X | X |
| X | X | O | O | O | O | X |
| O | X | O | X | X | X | O |
| X | O | O | O | X | O | X |
| X | O | X | O | O | X | O |

In this instance,

X scores 24 factors:

• $14times 1$ factors = $14$ factors (Connects 2)
• $5times 2$ factors = $10$ factors (Connects 3)
• it would not have any join 4 or extra

O scores 38 factors:

• $12times 1$ factors = $12$ factors (Connects 2)
• $5times 2$ factors = $10$ factors (Connects 3)
• $2times 4$ factors = $8$ factors (Connects 4)
• $1times 8$ factors = $8$ factors (Connect 5)
• it would not have any join 6 or extra

This is a big victory for O!

The puzzle asks: is Connect X a solved sport?

Note 1: if no reply is discovered for $(i,j,okay,l,m)inmathbb R_+^5$, I’ll completely settle for a solution for $(i,j,okay,l,m) = (1,2,4,8,16)$ 😀

Note 2: You can simply discover that the trivialization given by @Trenin just isn’t legitimate for Connect X!