Square Square
April 10, 2018
We have today an opportunity for some code golf:
Write a program to find a four-digit positive integer that, when multiplied by itself, contains the original four-digit number in the last four digits of the product.
Your task is to write a program to find the desired number. If you wish, you can take it as a challenge to use the minumum number of symbols in your programming language. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.
Programming Praxis 
Perl being the true golfing language!
[sourcecode]
perl -E’say grep{$_**2=~/$_$/}1000..9999′
[/sourecode]
Perl being the true golfing language! – just realised 2 bytes too long!
perl -E’say grep{$_**2=~/$_$/}1e3..1e4′Python 3
for i in range(10**3, 10**4): if i**2 % 10**4 == i: print (i**2, i)87909376 9376
Julia implementation (comprehensive & extensible version):
ContainsOriginal(x::Int64, X::Int64) = string(x) == string(X)[end-3:end]
for x = 1001:9999
if ContainsOriginal(x, x^2); println(x); break; end
end
result: 9376 (after about 0.001 sec, with about 42K memory allocations)
Here’s a version in Basic that is well-suited to that language:
10 PRINT 87909376
Klong version
f::{[l];l::[];{:[((x*x)!10000)=x;l::x,l;""]}'x; l} :monad f(3164+!(10000-3164)) [9376]Mumps version
9376
Hats off 2 Perl. Your golfing skills are beyond compare!
Here’s a Haskell version in the ghci REPL. Not much golfing; only the removal of spaces.
Didn’t we do something like this recently? https://programmingpraxis.com/2016/06/28/curious-numbers/
Anyway, here’s an anti-golf solution to the present problem, using TensorFlow (I’m just learning so this might be a terrible way to solve the problem):
import tensorflow as tf def fn(previous, current): return tf.cond(tf.equal(current*current%10000,current), lambda: current, lambda: previous) elems = tf.Variable(list(range(1000,10000))) initializer = tf.constant(0) out = tf.foldl(fn,elems,initializer=initializer) with tf.Session() as sess: sess.run(tf.global_variables_initializer()) print(sess.run(out))Python 3 version in 46 characters:
[x for x in range(1000,10000) if x*x%10000==x]
Add `[0]’ for 49 characters if it needs to return an int instead of a list.
Python 3:
I see some people have found the solution by finding the modulus with 10**4, thats probably more efficient than what I did, I found the last 4 digs of the square by converting to a list and indexing.
for i in range(103, 104):
sqr = list(str(int(i**2)))
lis = list(str(i))
if lis[:] == sqr[len(sqr) – 4:len(sqr)]:
print(lis[:])
For the range I meant 103, 104, it changed it for some reason and made it bold.
ugh, I mean 10 ^ 3, 10 ^ 4
Here’s a solution in Python. It uses depth-first-search to incrementally construct a valid 4-digit number.
def search(): stack = [[1], [5], [6]] while stack: digits = stack.pop() count = len(digits) number = int(''.join(map(str, digits))) if (number**2) % (10**count) != number: continue if count == 4: return number for i in range(1,10): stack.append([i] + digits) return None print search()Output:
((1000 to: 9999) select: [:x | x*x\10000 = x]) first “Smalltalk”
I typed x*x\10000 with two backslashes, honest.
Bash
$ for i in {1000..9999}; do (( i * i % 10000 == i )) && echo $i; done 9376ClojureScript