Cryptogram ♥♥ 2

Logic Level 3

P Q R S ∗ 4 = S R Q P PQRS * 4 = SRQP

Find ( S ∗ R ) ( Q ∗ P ) (S*R)^{(Q*P)} , provided P,Q,R,S are distinct real numbers.


The answer is 3136.

Satyabrata Dash by Satyabrata Dash , 20, India

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2 solutions

Rajdeep Brahma
Mar 24, 2017

PQRSX4=SRQP S being multiplied by 4 gives last digit P. So , P is even. Now a 4digit no. on being multiplied by 4 gives a 4 digit no. if it starts with 1/2. P=2. S=8/9.If S=9,then SX4=36 or,P=6 (contradiction). So,S=8. (2000+100Q+10R+8)X4=8000+100R+10Q+2 Simplifying,390Q=60R-30 or,13Q=2R-1 Now R<10.So 2R-1<19. So,13Q=13(Since Q is a natural no.) This gives Q=1 & R=7 ANSWER=(8X7)^(2X1)=3136

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As far as I know, code is THE best way to solve cryptograms: 

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from itertools import permutations

for p,q,r,s in permutations('0123456789',4):
  if int(p+q+r+s)*4==int(s+r+q+p):
    print((int(s)*int(r))**(int(q)*int(p)))


1
 
3136

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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