Do you mean you can find the revised standard deviation without knowing how many samples there are to begin with? If so, perhaps I'm misunderstanding your original question. Would you post the equations?
(after "Similarly for sample standard deviation:")
after working out a new mean by simply "((num_of_samples X old_mean) -removed_value)/(num_of_samples - 1)" it should be possible to work out a new 's' by solving first to find the "old" summation of the squares and then using it as "result of the summation of the squares minus square of the removed value". (because the main problem is that we don't know the individual squares since we don't know the values but we may be able to find their summation)
If you know the old standard deviation, old mean, original number of sample, and the sample to remove, it's possible to find the new standard deviation.
There was just some confusion because you did not mention knowing the original number of samples in the problem statement. If you do not know the original number then you cannot determine the new standard deviation.