One day my friend Dorsey told me from LA, that he gets the same salary in each month but when he adds up his six figure salary of two months, three months, four months, five months, or six months each time the figures (or digits) of his salary remains the same, but not in a fix order. Later, he told me that when he add up his salary of 7 months his total salary become`(10^6 - 1)`. What is the salary of Dorsey?

Options

A. a. 123456
B. b. 285614
C. c. 142857
D. d. can't be determined

Answer

To solve the problem, we need to find Dorsey's monthly salary based on the information provided. Let's break it down step by step.

### Step 1: Understand the total salary for 7 months
Dorsey mentioned that when he adds up his salary for 7 months, it equals \(10^6 - 1\).

\[ 10^6 - 1 = 1,000,000 - 1 = 999,999 \]

So, Dorsey's total salary for 7 months is \(999,999\).

### Step 2: Calculate the monthly salary
Since Dorsey receives the same salary each month, we can find his monthly salary by dividing the total salary for 7 months by 7.

\[ \text{Monthly Salary} = \frac{999,999}{7} \]

Calculating this gives:

\[ 999,999 \div 7 = 142,857 \]

### Step 3: Verify the conditions
Now, we need to verify if the monthly salary \(142,857\) meets the condition that when multiplied by 2, 3, 4, 5, or 6, the digits remain the same but in a different order.

- For 2 months:
\[ 142,857 \times 2 = 285,714 \]

- For 3 months:
\[ 142,857 \times 3 = 428,571 \]

- For 4 months:
\[ 142,857 \times 4 = 571,428 \]

- For 5 months:
\[ 142,857 \times 5 = 714,285 \]

- For 6 months:
\[ 142,857 \times 6 = 857,142 \]

In each case, the result is a six-figure number with the same digits as \(142,857\) but in a different order.

### Conclusion
Thus, Dorsey's monthly salary is:

\[ \boxed{142,857} \]