Discussion
How many odd numbers which are immediately preceded by perfect cube and followed by perfect square ?
Answer: C
There is 1 such odd number.
Among single digits, the perfect cubes are 1 and 8, and the perfect squares are 1, 4 and 9. An odd digit is needed with a cube just before it and a square just after it.
The only place this happens is 8 3 1 at positions 6, 7 and 8: 3 is odd, 8 before it is a cube (\(2^{3}\)), and 1 after it is a square. Every other odd digit fails on one side, for example the 3 at position 16 has 1 before it but 5 after it.
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