Question 1156837
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Tutor @ikleyn, while she write many excellent responses to readers' questions, is not expert in the English language.  Her contention that there is no answer to the question is not correct.  The phrase "next smallest" is different from "smallest".<br>
The other tutor shows what is almost certainly the EXPECTED answer: -8 is the next integer smaller than -1 that is a perfect cube.<br>
However, grammatically the phrasing of the problem is at best confusing, and possibly completely incorrect.<br>
Think about what the phrase "next smallest" means. You have, say, a bunch of spheres of different sizes.  There is a smallest sphere; and then the "next smallest" is one that is slightly LARGER than the smallest.<br>
So then the question seems to be self-contradictory in saying that we are looking for THE NEXT SMALLEST integer that is LESS THAN -1.<br>
It is not surprising that you were stuck on this problem, given that it is poorly worded....<br>