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This line makes no sense at all

\(3^3 \cdot 2^3 \cdot 1^3 = 27 \cdot 8 \cdot 1 = 216.\)

There are 3 choices for the first A then 2 choices left for the second A then only on spot left fot the third A  that is 3! places not 3^3 places.

Normally powers are only appropriate for replacement questions.

I drew a diagram, and got GM = 2 and GA = 5, so I think the answer is 2/5.

just curious, why did you delete all your questions and answers? i found this after checking your profile...

Notice if you isolate y in both equations, you can get four different linear inequalities that you can graph.

So isolating:

\(\frac{-3-7x}{2}\leq{y}{\leq}\frac{3-7x}{2}\)

\(-4+x\leq{y}{\leq}4+x\)

Ok now we have:

Graph:

Notice the intersection shape of the FOUR inequality inequations.

The MAXIMUM value of x + y, which is the answer you are looking for, is the vertice FARTHEST away from the origin.

There can be two vertices that fit this, but they will end up giving you the same answer.

So all you need to do is find the coordinates of where two lines intersect. (they should intersect at the said vertice)

I will leave that up to you to find this.

I agree, Wonderman, you do not have the authority to do this.

The question asker may have not recieved sufficient help.

Who are you to tell me not to help this kid? 

The only reason I don't is that I don't know how. 

_.

Do these pictures give any ideas?

NOT D or A

This is a fun problem! Here is the pic:

Notice the red and green triangles. The red triangle has a base of 1 and a width of 2, based on Pytahgorean theorem, we can conclude it has a hypotenuse of \(\sqrt{5}\).

Notice how the red and the green triangles SHARE a hypotenuse.

We know that one of the legs of the green triangle has a length of 2. The red and green triangle share a hypotenuse, so knowing the green triangle's hypotenuse and one of its legs, we can conclude through the pythathoream theorem that the base of the triangle is 1.

With this information, the red and the green triangle have EQUAL areas.

We know the area of the RED triangle from the previous picture is 2 * 1 = 2/2 = 1.

Can you solve this? I know I can't. Help.

Precise answer has been deleted by melody,

https://www.youtube.com/watch?v=1rDVz_Fb6HQ 

thank you for explaining. could you show me where my reasoning went wrong? i would like to know how i could fix it next time.

It might be 1/5??

because i'm assuming that the two golden parts on the overlapping triangle equal 1/2 of the overlapping triangle

because the golden parts overlap, the area is not counted twice so therefore there would be 5 halves and since the two golden triangles make one half of the rectangle(that's an assumption!!) so it would be one out of five halves are golden

once agaain i am very unsure of whether that logic is reasonable or not but i believe it's somewhat correct

The lattice I have given is precisely the set of points we are looking for. But a proof is wanting.

(Notice that 'our friend with the few words of encouragement' who said to my partitions "bits iss wrong" has packed his bags and left the ring. That to me is an indication that he/she has either run out of words completely or that I have happened to hit the jackpot with my poorly dotted diagram of the terminal points. Have we been mean to him/her, perhaps? Is it possible that English is his/her third or fourth tongue, and that that tongue is still developing? I remember a long time ago as an exchange student I developed an intense dislike  for anyone who expected me to talk with more words than the vocabulary of a parrot contains. In fact for about 6 months after arrival I hardly opened my mouth. I guess I was waiting for the moment of glory, when my English would suddenly become bedazzlingly fluent and my voice commanding and irresistable. Of course that never happened, but I manage and yet still have very little to say.)

I am still looking for the overlapping partitions though even though I am becoming convinced that that approach is suffering from a fundamental  flaw; there are too many overlaps and not enough partitions to cover all 221Points.

PLEASE do not post AoPS homework problems on this forum. If you need help, use the online message board, as posting questions on this forum is violating their code of conduct.

Each person gets half an apple

thanks 

Correct, shgg111....!!!!

I do! Thanks to Guest.

thank you 

the other one is (x+3)^2  +  (y+4)^2 = 25   right ?

Nice work!

....I have no idea if your answer is correct...There may be multiple answers for a b c d ...BUT question asks for MINUMUM value of a+b+c+d

You're welcome....I hope you understand the answer ! 

There are two,

here is one   x=3   y = -4      h,k is then   3,-4

(x-3)^2  +  (y+4)^2 = 25           can you find the other one?

Awesome dude, thanks!