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Even and Odd Products (Posted on 2023-08-07) Difficulty: 3 of 5
Find two different 5-digit numbers, each containing 5 different even digits, whose product is a square.

Do the same for odd digits.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Solution Computer Solution Comment 1 of 1
46208 * 64082 = 2961101056 = 54416^2
19375 * 57319 = 1110555625 = 33325^2

--------------
def issquare(n):
    """ Input an integer, Returns True iff it is a perfect square. """
    if round(n**0.5)**2 == n:
        return True
    else:
        return False

odddigits = '13579'
evendigits = '24680'
odds = []
evens = []
from itertools import permutations
from itertools import combinations

for perm in permutations(odddigits):
    p = ''.join(perm)
    odds.append(int(p))
for perm in permutations(evendigits):
    if perm[0] == '0':
        continue
    p = ''.join(perm)
    evens.append(int(p))

for comb in combinations(evens,2):
    a = comb[0]
    b = comb[1]
    if issquare(a*b) :
        print('{} * {} = {} = {}^2'.format(a,b,a*b,int((a*b)**.5)))
        
for comb in combinations(odds,2):
    a = comb[0]
    b = comb[1]
    if issquare(a*b) :
        print('{} * {} = {} = {}^2'.format(a,b,a*b,int((a*b)**.5)))

  Posted by Larry on 2023-08-07 08:16:51
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