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
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