Advent calendar 2021
22 December
There are 12 ways of placing 2 tokens on a 2×4 grid so that no two tokens are next to each other horizontally, vertically or diagonally:
Today's number is the number of ways of placing 2 tokens on a 2×21 grid so that no two tokens are next to each other horizontally, vertically or diagonally.
Show answer
Hide answer
The two tokens must be in two non-adjacent columns. There are ½×21×20 ways of picking two different columns. 20 of these ways will give two adjacent columns,
so there are ½×21×20–20=190 ways to pick the columns.
Once the columns are picked there are four choices for the rows to place the tokens in (up and up, up and down, down and up, down and down). 4×190=760.
