Thanks! i think i kinda got it. Using your way of assuming there are 100 pollywogs and 100 flies, i figured that 17x7=119 which is bigger than 100, so each consuming 7% of the total amount would be impossible. 😅 and that 7%was probably compared to their previous consumption. 😊

@authenticcrane If I recall correctly, stars and bars is for both indistinguishable items. Thus your reasoning as to why it is 7 choose 2 is correct. Unfortunately, I do not think you can manipulate stars and bars for items that are distinguishable.

Hi, not a particular geometry pro, but i hope i can help.😊 WechatIMG2.jpeg

Screen Shot 2022-08-27 at 11.09.12 AM.png
Great question!! I've attached a diagram to make things clearer and I'll try to explain it here.

[Left column] first of all, as you can see, if you graph out all six solutions of (x,y), it forms this region shaped like an isosceles triangle-- in fact, it's a right isosceles triangle with side length 2 (white shaded). The solutions to this question are precisely the lattice points (points with integer coordinates) that are contained within that triangle!

But why is that?

[Right column] Well, if you think about it, we start out with a whole lattice grid of possible (x,y). That includes stuff like (x,y) = (-45840, 409574) or (x,y) = (0,0) or (x,y) = (1,2), etc etc etc. In order to narrow down this infinite # of possible (x,y) into the actual solutions, we need to consider the three constraints on (x,y):

first of all, x >= 1. That's because the problem says that x should be a positive integer, which means it can be 1, 2, 3, ....

second of all, y >=1. That's because y also has to be a positive integer.

Finally, we must have x + y <= 4 by the problem statement.

The basic idea for the algebraic solution is to graph out what each of these three constraints looks like, and "combine" them together. So if you look at the graph for x >= 1, we've shaded all points (x,y) such that x >= 1. Similarly, the pink shading represents all the points such that y >= 1. And the blue shading represents all the points such that x + y <= 4 (to do that, we first graphed the line x + y = 4, and then we shaded in everything underneath it!)

So now we have three different graphs of shaded regions, each representing different conditions. If we want ALL THREE conditions to be satisfied, all we have to do is "overlay" the graphs on top of each other and figure out what region is shaded in all three graphs! And if we do so, we see that the light yellow triangle is the region of overlap. Therefore, all the lattice points inside that triangle are the answer.

Hope this made sense to you, and feel free to reach out if you have any further questions! 😄

@audrey Thanks! Your explanation has helped.

I got it.

@enlivenedporcupine-0 Yeah that's CSS web development add just skip it sir.

@Desolate_101 I made that using Python and In python I used Tkinter. If you can contribute to this project you or wana tell me something you can contact me a this email : harshsc2007@gmail.com.
Thank you for checking out my project. After 1 year some one has sent some reply. And now I have stopped development on my project cause of studies. if you want to develop you can contact me at above email and if you want we can partnership in coding. on projects

Thank You
Harsh

yeah, i think it would better if they mentioned something. but usually questions like that are a follow-up of the your turn problem or else the problem would be meaningless. 😆

@genuineopossum to clarify, 9 is supposed to be (10-x) for 1 and 8is supposed to be (10-x) for 2 and so on.

@audrey said in Module 0 Week 3 Challenge Q20:

@fantasticcrow Yay, I'm glad that helped!! And as for counting versus probability, it all depends on what the question asked for. To give a simple example:

How many ways are there to make a three digit number where all the digits are even? [This would be a counting problem, because you want to count how many 3-dig #'s there are where all the digits are even]

Vs.

If you choose any three digit number at random, what is the probability that all its digits are even? [This would be a probability problem, because you're asked what the chance of something happening is-- so in this case, you would take the answer from #1, and divide by how many three digit numbers there are!]

In the context of this problem, we can't use simple counting because not all of the options are equally likely to be chosen. In other words, you should use counting when all the options are equally likely ("weighted")-- for example, choosing a three digit number at random. But in this case, they're not, so we have to actually multiply out probabilities, if that made sense.

Very helpful. Thank you!

@lucky_ducky1 thanks! you gave a great explanation.

-1x-2+3-4+(5x6-7^2)- -18=?

@RZ923 wait... What???? Prof.Loh = Married ???

@excitedarmadillo-0 No, it is just the same test, it doesn't change