

Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:

 What is the smallest positive integer whose square ends in the digits 269,696?

— Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.

He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.



Task[edit]
The task is to find out if Babbage had the right answer — and to do so, as far as your language allows it, in code that Babbage himself would have been able to read and understand.
As Babbage evidently solved the task with pencil and paper, a similar efficient solution is preferred.

For these purposes, Charles Babbage may be taken to be an intelligent person, familiar with mathematics and with the idea of a computer; he has written the first drafts of simple computer programmes in tabular form. [Babbage Archive Series L].



Motivation
The aim of the task is to write a program that is sufficiently clear and well-documented for such a person to be able to read it and be confident that it does indeed solve the specified problem.




IDENTIFICATION DIVISION.
PROGRAM-ID. BABBAGE-PROGRAM.
* A line beginning with an asterisk is an explanatory note.
* The machine will disregard any such line.
DATA DIVISION.
WORKING-STORAGE SECTION.
* In this part of the program we reserve the storage space we shall
* be using for our variables, using a 'PICTURE' clause to specify
* how many digits the machine is to keep free.
* The prefixed number 77 indicates that these variables do not form part
* of any larger 'record' that we might want to deal with as a whole.
77  N           PICTURE 99999.
* We know that 99,736 is a valid answer.
77  N-SQUARED   PICTURE 9999999999.
77  LAST-SIX    PICTURE 999999.
PROCEDURE DIVISION.
* Here we specify the calculations that the machine is to carry out.
CONTROL-PARAGRAPH.
    PERFORM COMPUTATION-PARAGRAPH VARYING N FROM 1 BY 1
    UNTIL LAST-SIX IS EQUAL TO 269696.
    STOP RUN.
COMPUTATION-PARAGRAPH.
    MULTIPLY N BY N GIVING N-SQUARED.
    MOVE N-SQUARED TO LAST-SIX.
* Since the variable LAST-SIX can hold a maximum of six digits,
* only the final six digits of N-SQUARED will be moved into it:
* the rest will not fit and will simply be discarded.
    IF LAST-SIX IS EQUAL TO 269696 THEN DISPLAY N.