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jmc

number theory junior

Problem

There are twenty-four -digit numbers that use each of the four digits , , , and exactly once. Listed in numerical order from smallest to largest, the number in the position in the list is
(A)
(B)
(C)
(D)
Solution
For each choice of the thousands digit, there are numbers with that as the thousands digit. Thus, the six smallest are in the two thousands, the next six are in the four thousands, and then we need more numbers. We can just list from here: .
Final answer
B