The new number is 3*(11k + 4) = 33k + 12, and 12 mod 11 = 1.

The new number is (7k + 3 + 4) = 7k + 7, which gives a remainder of 0 when divided by 7.

The smallest number satisfying both conditions is 22.

29 gives a remainder of 2 when divided by 9 (9*3 + 2 = 29).

The remainder is 3, as 5k is divisible by 5.

The smallest number satisfying both conditions is 9, as 9 mod 4 = 1 and 9 mod 5 = 4.

The smallest number satisfying both conditions is 12, as 12 mod 5 = 2 and 12 mod 7 = 5.

20 leaves a remainder of 4 when divided by 8 (8*2 + 4 = 20).

The number can be expressed as 12k + 5. When divided by 4, the remainder is 5 mod 4, which is 1.

17 leaves a remainder of 5 when divided by 12 (12*1 + 5 = 17).

The number can be expressed as 10k + 7. When divided by 5, the remainder is 7 mod 5, which is 2.

The remainder when 123 is divided by 10 is 3, as 123 = 10*12 + 3.

1000 divided by 6 gives a quotient of 166 and a remainder of 4.

145 divided by 12 gives a remainder of 1.

250 divided by 7 gives a quotient of 35 and a remainder of 5.

256 divided by 7 gives a quotient of 36 and a remainder of 4.

The sum of the digits of 987654 is 39, which is divisible by 9, hence the remainder is 0.

1000 divided by 6 gives a remainder of 4.

Since 6 mod 3 = 0, the remainder when the number is divided by 3 is also 0.