@tomrocksmaths: Can you solve the mutilated chessboard problem? Originally posted by Martin Gardner in Scientific American in 1957, it asks whether a chessboard with opposite corners removed can be covered completely using dominoes? Thanks to Dr Garth - YouTube’s Head of Health - for being such a good sport! #tomrocksmaths #scientificamerican #martingardner #chessboard #mathspuzzle

H V :

it's a pairity issue

🌹🌹🌹 :

Before watching the video: at first i thought yeah, each domino covers 2 squares 62/2 =31 so you could use 31 domino’s. But each domino covers 1 dark and 1 light square no matter if it’s vertical or horizontal, by removing 2 light squares there is an imbalance of light and dark squares meaning you can’t cover the whole board

❯❯❯❯❯ Max ⚓︎ :

Nat Pitcher :

That is excellent reasoning with the “each covers 1 red and 1 white.” Brilliant :)

Atambob :

in the first video he states, "a domino is gonna cover two squares" the way he says it sound like he is clarifying the size of the donimo to the chessboard squares rather stating 1 donimo has to cover 2 squares. with that thinking, 1 donimo does not have to cover 1 black and 1 white square. he also never states anything about overhanging. so you could use the same 32 donimos to cover the entire chessboard. I go by the letter of the law, and his wording is pretty vague

Vasco Silva :

can't see why not. 2 dominoes will stand on only half the surface but they will still cover the whole board.

finleycoops :

Not possible since the corner squares are the same colour. Meaning 31 dominoes have to cover 30 of one colour and 32 of the other. Whereas 31 domino’s can only cover 31 of each colour

O :

Given how the question is posed I'd just put the dominos down exactly the same as it hasn't specified that it's not allowed to go over the edges. Or I'd just stack dominos on each other to cover the board.

Gerard Daniel | Notion :

Did he say we couldn't place at least a piece diagonally? The math proves we need 31 dominoes but given the location of the mutilated squares, one of the 31 dominoes would need to be diagonal to cover everything.

Dn Dave :

every domino covers a red and a white square and because you remove 2 squares of the same colour there will be no possible way to put the 31 (62/2) dominoes to cover all squares

mrsuri :

Regardless of which 2 squares are removed, 32 dominoes is still the answer

Sacideminas 🍉 :

No stated rule that a domino can’t hang off the edge of the board so you can cover the board with the missing squares with the same method as the full 64 squares. Two dominos will cover only one space each and hang off the edge.

Dan :

Tom, next question, can you remove 1 white and 1 red from ANY combination of positions and still cover the board?

handfeddog :

This problem taught me about coloring as a problem solving technique. It's much harder if you don't draw it with the black and white coloring.

srboss23 :

much more elegant to think in terms of colour than the way i thought about it. I figured that this would leave a row with 7 on, which to cover youd need a vertical (or perpendicular to others) domino, which would eat into the other row causing 7 to be in the next row, and so on until you reach the edge where there is no row to eat into,

kevv :

No because 1 domino covers 1 red and 1 white tile but he removed 2 white tills so there will always be 2 red tiles left over

Queque :

1st

- :

Aaaaaahhhhhh🥰🥰🥰

Shawn :

pidgeonhole principle

th3dog616 :

i try wild i saw the video in my head i got 29

Why :

31

Lspacenl :

But you did not put in a rule that all dominoes must be completely on the board.

Cal Coleman :

Start in the middle

ClintLagorra :

if you just need to cover it, then YES.😂