Rosetta: Babbage problem

[bartc]

On 09/05/2017 13:56, Robert L. wrote:
>> 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
>>
>> 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.


> (use srfi-121)
>
> ;; Create function that accepts a number and returns
> ;; true if, only if, it satisfies the requirements.
> (define (good? n) (equal? 269696 (modulo (* n n) 1000000)))
>
> ;; A generator for the natural numbers (1,2,3,4 ...).
> ;; Each time it is called, it yields the next number.
> (define generate-naturals (make-range-generator 1))
>
> (generator-find good? generate-naturals)
>
>  ===>
> 25264
>
> -----
>
> (use lazy-lists)
>
> (define (good? n) (equal? 269696 (modulo (* n n) 1000000)))
>
> (First (Filter good? (Cardinals)))
>
>  ===>
> 25264


This time I know this is not Python! This is easy to solve by 
brute-force as we know the answer is small:

i=0
while 1:
     if (i*i) % 1000000 == 269696:
         print ("Found:",i)
         break
     i+=1

I think Babbage would have had a better chance of understanding this 
than whatever was used above.

(There was a short-lived language actually called 'Babbage', which I 
once implemented, although I doubt the man himself would have made much 
of it. But he might have been p*ssed off that it wasn't quite as 
successful as 'Ada', named after his programmer.)

-- 
bartc