Reverse Cryptogram

Logic Level 3

X A + B X Y X A × B Y X \begin{array}{ccccc} & & & & X & A \\ + & & & & \ &B \\ \hline & & & & X & Y \\ \hline \end{array} \qquad \qquad \begin{array}{ccccc} & & & & X & A \\ \times & & & & \ &B \\ \hline & & & & Y & X \\ \hline \end{array}

Given that A , B , X A,B,X and Y Y are distinct non-negative integers satisfying the two cryptogram above. Find the value of the 2-digit integer X Y ‾ \overline{XY} that is not equal to 27.


The answer is 49.

Jack Sacks by Jack Sacks , 18, United Kingdom

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2 solutions 

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from itertools import permutations

for x,a,b,y in permutations('0123456789',4):
  if int(x+a)+int(b)==int(x+y) and int(x+a)*int(b)==int(y+x):
    if x=='2' and y=='7':
      continue
    else:
      print(x,y)


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49

0 Helpful 0 Interesting 0 Brilliant 0 Confused

We let 47 + 2 = 49 and 47 x 2 = 94. Then X = 4, A = 7, B = 2 and Y = 9. Therefore XY = 49.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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