The 4-digit numbers less than 2000, formed by digits 1, 2, 3, and 4 without repetition, must start with the digit 1. The remaining three digits (2, 3, 4) can be arranged in 3! = 6 ways. The sum of these 6 numbers can be calculated by considering the sum of digits in each place value. The digit 1 appears in the thousands place for all 6 numbers. The digits 2, 3, and 4 each appear in the hundreds, tens, and units place an equal number of times, which is 6 numbers / 3 digits = 2 times. The sum of the digits (2+3+4) is 9. Therefore, the sum is (1 * 1000 * 6) + (9 * 100 * 2) + (9 * 10 * 2) + (9 * 1 * 2) = 6000 + 1800 + 180 + 18 = 7998.