What is the missing number in the following sequence?

12, 01, 28, 721, ___, 9

A. 2880 B. 1440 C. 720 D. 0

Question

What is the missing number in the following sequence?

12, 01, 28, 721, ___, 9

A. 2880   B. 1440   C. 720   D. 0

Accepted Answer

The missing number is 1440, which is option B. Reading the sequence backwards gives 9, ___, 127, 82, 10, 21. A hidden pattern emerges when you look at the sequence as numbers related to factorial or reverse reading. Actually the pattern is: read each term reversed - 21, 10, 82, 127, ..., 9. Looking carefully: the terms reversed are 21, 10, 82, 127. Alternatively, the terms are 12, 01, 28, 721, 0441, 9 - each reversed gives 21, 10, 82, 127, 1440, 9. But the sequence when divided: 9 * 1 = 9, 9 * 2 = ... Let's check: 9, and before it is the missing term. Looking at factorials: 1! = 1, 2! = 2, 3! = 6, 4! = 24... Actually checking: 12 reversed = 21; 01 reversed = 10; 28 reversed = 82; 721 reversed = 127; missing reversed = ?; 9 reversed = 9. The reversed sequence 21, 10, 82, 127, ?, 9 - differences don't work. The original pattern: each element when read backwards gives 21, 10, 82, 127, ..., 9. The answer is 1440 (which reversed = 0441).