jfan17

-GA

First of all, if I was really talking from an unknowledgeable perspective, what is your rationale behind me not noticing the logical fallacy presented by Cal? This makes no sense whatsoever. Cal tells us that :

"

The largest power of 2 that divides 20! is 2^18 .

The largest power of 3 that divides 20! is 3^8. 

We want the largest value of n that n is less than or equal to 8.

"

If I really had no knowledge of Legendre's formula like you so eagerly recommended, how would I have known anything about this kind of reasoning? If I was really uneducated and was looking at the steps Cal used as opposed to just the answer, I would've said "wait, how does this logic follow through"? Because if I didn't know anything about the subject, then I wouldn't have understood those last two lines at all. Your assumption here is just blatantly false.

Secondly, sure, say I buy your argument that there are many solutions on this forum presented from a knowledgeable perspective. Does that mean we should present all of our solutions from "a perspective that requires knowing the answer"? No, it does not by any means make us assume that our question-askers know what we're talking about. Rather, we should go through each step and explain the logic behind it. I'd argue that this is comparatively better than making them "learn the rote mechanics, and then the logic behind the process" themselves as you advocate for, because when we show question-askers the logic and decision-making calculus behind our steps, that allows them to go forward with more knowledge to tackle different types of these problems, which they can always combine with a bit of self-learning. We shouldn't just post the answer with logical leaps and expect our readers to understand. 

Thirdly, it was a mistake on my part to not fully explain Legendre's as you mentioned, however, I'm not trying to rip "Cal a new one for her incompetence", I'm trying to help her so she doesn't post misleading solutions that she doesn't fully understand; that just causes confusion for the question askers and everyone in general. 

Some parts of the problem are missing

No? That doesn't explain anything. Please understand your solutions before you post them! You're still not explaining WHY you have n less than or equal to 8...... if I was talking from an uneducated perspective, I would have NO idea with your logic jumps like that

I believe Cal took their explanation from the best answer on this website, it may help you understand the context:

https://stats.stackexchange.com/questions/193554/problem-understanding-the-following-probability-problem

We can write the equation:

(x-4) * (2y-1) = 1 +x*y 

which is what the problem gives us

It then asks us to find xy

Let's expand out the left side first. We get:

2xy-x-8y +4 = 1 + xy

Grouping everything on one side, we get:

xy - x - 8y + 3 = 0

Now, we can make handy of a principle known (on aops' forum at least) as "simon's favorite factoring trick", or "completing the rectangle".

if we add 5 on both sides, we can factor the left hand side, into:

(x - 8 ) * (y - 1) = 5

The problem then becomes a lot simpler, since 5 has two integer factors: 5 and 1

Let's assume x - 8 = 5 and y - 1 = 1

Then we have:

x = 13

y = 2

Clearly,  13>10, so this solution is not correct.

Let's assume the other case:

where,

x - 8 = 1

and

y - 1 = 5

Then we have:

x = 9

y = 6

Clearly, this fits our criterion, giving us the answers of 

9 * 6 = 54

Because his average for the four days was 90, that means his total score was 90 * 4 = 360, since average is defined in this context as:

(total score) / days played, which is

(total score) / 4 in this context

That means to get the total score, just multiply his average by 4, and we get 360 total score.

We already know his scores on the first 3 days, which were 93, 92, and 89 respectively. 

To get his score on the 4th day, we just have to add these up and subtract the sum from the total score, 360

We then get:

360-(93+92+89) = 360 - 274 = a score of 86 on the fourth day

Uh cal, that's not what a life insurance policy is, I think you kind of misunderstand. He's not talking about why a "life" is important, but rather "life insurance".

g =7

h = 5

Work out the value of 3g + 2h

This problem requires just substitution alone. We already know the values of g and h both, which are 7 and 5 respectively. If we substitute 7 for g, and 5 for h, we will get our desired answer. The expression of 3g + 2h then becomes:

3 * (7) + 2 * (5) 

This is equivalent to:

21 + 10 = 31