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I received the following:

Chose a number in the set: $\{1,2,...,8,9\}$ then:

$-$ multiple by $3$

$-$ add $3$

$-$ multiple again by $3$

$-$ add the two digits together.

After that we check the film's list to see what movies matches more with us.

$1.$ The Matrix

$2.$ The Big Lebowski

$\cdots$

$8.$ The Godfather

$9.$ You Starring in a Obscene Act

$\cdots$

Question: How does this work?

My interpretation:

$3(3a+3) = 10b+c \tag{1}$

where $a,b,$ and $c$ are one digits numbers. $b+c = 9$ but how to prove it?

My attempt: $3(3a+3) = 10b+c \implies a = b-1 + (b+c)/9$

$(b+c)/9$ must be integer , so $b+c$ is divisible by $9$, then it's $9$ or $18$. If it's $18$ then $a = b-1$, substituting in $(1) \implies c = -b$. I think this is not possible because of the negative sign, but I'm not sure.

Pinteco
  • 2,631

1 Answers1

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The number $9a+9$ is a multiple of $9.$ So the sum of their digits is a multiple of $9.$ Since $18\le 9a+9\le 90$ the only possibility is that the sum of the digits is $9.$ Thus the movie is "You Starring in a Obscene Act".

mfl
  • 29,399