The digits 1, 1, 2, 2, 3, and 3 are arranged to form an odd six digit integer. The 1's are separated by one digit, the 2's by two digits, and the 3's by three digits. What are the last three digits of this integer?
(A) 312
(B) 123
(C) 131
(D) 121
(E) 213
The digits 1, 1, 2, 2, 3, and 3 are arranged to form an odd six digit integer. The 1's are separated by one digit, the 2's by two digits, and the 3's by three digits. What are the last three digits of this integer?
(A) 312
(B) 123
(C) 131
(D) 121
(E) 213

## Solution

There are two numbers, either 312132 or 231213 that meet the given conditions. The requirement that the numbers must be odd, however, means that only the second number satisfies the requirements. The required answer is, '213'.