Predict Likes and Reshares?

Algebra Level 3

Start with any positive real number $n$ .

For every like that my next problem will get, multiply $n$ by $2$ .
For every reshare that my next problem will get, multiply 1 by the number you got in step 1 that many times.
Calculate $\log _{2}$ of the number you got in step 2.
Divide by the number of reshares my next problem will get.
Subtract the number of likes my next problem will get.
Take $2$ to the power of the number you got in step 5.
Finally, subtract $n$ from the number you have.

What is the result?

The answer is 0.

1 solution

Steven Yuan
Apr 29, 2015

It turns out that, regardless of the number of reshares and likes my next problem will get (as long as both are positive integers), the result is still the same.

Let $l$ be the number of likes and $r$ be the number of reshares. Here are the steps:

We get $n \cdot 2^l$ .
We get $(n \cdot 2^l)^r = n^r \cdot 2^{lr}$ .
We get $\log_{2} (n^r \cdot 2^{lr}) = \log_{2} n^r + \log_{2} 2^{lr} = r \log_2 n + lr$ .
We get $(r \log_2 n + lr)/r = \log_2 n + l$ .
We get $(\log_2 n + l) - l = \log_2 n$ .
We get $2^{\log_2 n} = n$ .
We get $n - n = \boxed{0}$ .

For step 2: For every reshare that my next problem will get, multiply the number you got in step 1 by itself that many times.

Say, his next problem only got 1 reshare, which makes r = 1. There are two points that don't seem to agree with each other

According to the wording of the problem, I would need to multiply my result in step 1 by itself once, thus squaring it.
Using your equation at number 2, the equation would be $(n \cdot 2^{l})^{1}$ after substituting in r = 1.

Kindly explain.

Philip Pati - 6 years, 1 month ago

Would it be better if I stated "multiply 1 by the number in step 1 that many times"?

Steven Yuan - 6 years, 1 month ago

Predict Likes and Reshares?

The answer is 0.

1 solution

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