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Remove last three to get cube root (Posted on 2014-02-11) Difficulty: 3 of 5
Let n be a positive integer. By removing the last three digits of n, one gets the cube root of n. Find a possible value of n.

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution Solution | Comment 1 of 3
The first thing to do is narrow it down by finding the numbers that become 3 digits shorter when their cube root is found.
The cube roots of 10000 and 99999 are about 21.5 and 46.4
This narrows it down nicely as the cube root must be from 22 to 46 and near the middle.
30^3 = 27000
is just a little too small
31^3 = 29791
still to small
32^3 = 32768 <----- got it

33^3 = 35937
which is too big.

  Posted by Jer on 2014-02-11 10:43:09
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