Rainbow Lego Blocks and Pattern Combinations

[tuckerkao]

I could use a formal proof going by the circle and expansions of it in the grid, but I will have to construct it myself, I am not greedy ^_^

Within only 3 knight jumps, it's possible to hop a knight into any of the 4 adjacent squares on the 8x8 board, thus explain why the knight has the potential to travel to all the squares if the board is big enough.

Jumping to any adjacent square is possible, most within only 3 moves, except 5 moves between the 2 middle grid due to the lack of space -

Spoiler Knight 3 Jumps Pattern :

 

[tuckerkao]

It's not ultra-hard actually, neither it requires usage of decimal/dozenal bases. Most players don't bother to learn it because this ending occurs extremely rare in practical games.

The King-Bishop-Knight checkmate occurs in 1/6000 games, however it's a rare possible way for an amateur player to screw up a professional player.

Spoiler Decimal 1 to 10 Additions Pattern on Lego Plates :

Spoiler Decimal 11 to 20 Subtractions Pattern on Lego Plates :

 

[Narz]

The King-Bishop-Knight checkmate occurs in 1/6000 games, however it's a rare possible way for an amateur player to screw up a professional player.

I've had it one time out of probably 50,000 games or so (online and in person)

I managed to win

 

[Manfred Belheim]

I've read page 1 and page 7 of this thread and I'm beginning to suspect I may still be asleep.