Find the sum of all four-digit numbers that can be made using thedigits 1, 2, 3 and 4 without restriction.

To solve this problem, we need to consider that each of the four digits (1, 2, 3, 4) will appear in each place-value (thousands, hundreds, tens, ones) the same number of times in all possible four-digit numbers.

1. There are 4^4 = 256 total four-digit numbers that can be made using the digits 1, 2, 3, and 4 without restriction.

2. Each digit (1, 2, 3, 4) will appear in each place-value (thousands, hundreds, tens, ones) 256/4 = 64 times.

3. The sum contributed by the ones place is 64*(1+2+3+4) = 640.

4. The sum contributed by the tens place is 10 times the sum contributed by the ones place, so it's 640*10 = 6400.

5. Similarly, the sum contributed by the hundreds place is 640100 = 64000, and the sum contributed by the thousands place is 6401000 = 640000.

6. The total sum of all these four-digit numbers is 640 + 6400 + 64000 + 640000 = 707040.