(i) Is there a number which when divided by 3 gives a remainder of 1; when divided by 4 gives a remainder of 2; when divided by 5 gives a remainder of 3; and when divided by 6 gives a remainder of 4? If so, what is the smallest such number?

(ii) Suppose x is an integer such that 0 ≤ x ≤ 5. Is there a number which when divided by 6 gives a remainder of 6-x; when divided by 7 gives a remainder of 7-x; when divided by 8 gives a remainder of 8-x; and when divided by 9 gives a remainder of 9-x? If so, what is the smallest such number (in terms of x)?