The numbers 1 to 25 are to be placed on a black and white 5x5 grid so that each number, except 1, is next to (horizontally or vertically), the number one less than itself. eg.

http://i11.tinypic.com/6badc07.jpg
a) Explain why number 1 must be placed on a black square

b) Explain why the numbers 1, 3, 5, 7, 9 can not all be placed on one long diagonal

c) Show that in a completed numbering the sum of the numbers on a long diagonal must be at least 33 and that 33 can occur.

Any help is appreciated!

Thanks!