Gschill

I have thought alot about it but i still have had no success.. please help me .

Numbering Squares: The numbers 1 to 25 are to be placed on a black and white ( like a checker board) 5 X 5 grid so that each number, except 1, is next to, horizontally or vertically, the number one less than it. (note: all the corners are black squares) a. Explain why the 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.

Hi , these were my homework problems: I am keen in maths, but i am just not that good at it please help me. The number 53214 has five digits: 1,2,3,4,5. It has an unusual property. The number 532 is divisible by 4 ; the number 321 is divisible by 3 ; and the number 214 is divisible by 2. a. Show that the number 41325678 , which has eight digits 1, 2,.....,8, has a similar property: its first three digits form a number divisible by 7, the three digits following the first digit form a number divisible by 6, and so on. Let ABCDEFGH be an eight digit number where A,B,C,D,E,F,G,H are the digits 1,2,3,4,5,6,7,8 in some order. For example A= 4, B=1, C=3, D=2, E=5, F=6, G=7, H=8 gives the number in a. b. Find the other eight-digit numbers ABCDEFGH in which the three-digit number ABC is divisible by 7, the three-digit number BCD is divisible by 6, CDE is divisible by 5, DEF is divisible by 4, EFG is divisible by 3 and FGH is divisible by 2. Your answer should make it clear that you have found them all.