1) Find the binary (base 2), octal (base 8), and hexadecimal (base 16) expasion of 234567. 2) A 3 × 7 rectangle is divided into 21 squares each of which is colored red or black. Prove that the board...

1) Find the binary (base 2), octal (base 8), and hexadecimal (base 16) expasion of 234567.

2) A 3 × 7 rectangle is divided into 21 squares each of which is colored red or black. Prove that the board contains a nontrivial rectangle (not 1 × k or k × 1) whose four corner squares are all black or all red.