Elementary arithmetic, with brief notices of its history... by Robert Potts.

6
6. Find all the integral numbers which can be formed out of the
digits 0, 1, 2, 3, when one, two, three, four digits are taken respectively to form each number.
IV.
1. What methods did the ancient Greeks and tlomans adopt to
represent numbers? Were the Roman characters ever employed as
instruments of calculation, as the figures in the decimal scale of
notation?
2. From whence was the ordinary system of arithmetical notation
by nine figures and zero derived? About what period was it introduced into Europe? What system did it supersede, and when did it
begin to be generally used?
3. Define unit and number, and distinguish between abstract and
concrete numbers.
4. Explain clearly the difference between the intrinsic values of
each of the nine digits, and their local values in the denary scale;
and shew that, with the aid of the tenth character zero, these digits
are competent to express all numbers whatever, however great or
however small.
5. In the denary scale of numeration, how many different words
are employed in counting a million?
6. Give the derivation and explanation of the terms calculating,
counting, cipher, algorithm.
7. In the denary system of notation explain why the number of
digits cannot be more or less than the local value 10.
8. Specify clearly the advantages of the Indian method of arithmetic, (1) with respect to the powers of its notation, (2) of its operations.
9. State the considerations which render the sciences of number
aid space useful instruments for the training of the intellectual
powers.