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PATYUSH MAKKAR

1.(did we have to have 4 as a digit)

sol (not including 4 in some cases)BY the first constraint we have 0,1,2,3,4(remember that the last digit has to be 0)

case 1 – first digit 1- w get the sum of the digits as 1 now the 2nd digit has to be 2

case 2 -2 – has to be 1,4

case 3-3-has to be 0 or 3

case 4-4 – has to be 2

adding all the cases we get 6!

2. we use the multiplication principle of counting

let the rook be in a random place , since the second rook cannot be in the same column or row, we have 49 choices left for the second one thus there are 64 choices for the first one, 49 for the second one. Repeating the process until we have 0 places left we get 8 rooks.

3. by doing casework and looking at possible transformations we get the total as 55