Do you have any path questions where the starting point is the bottom left of some gridded shape and the top right is the endpoint? I want to practice these so that I don't have to spend a lot of time on them in competitions and so that I can get some of my friends to do math outside of syllabus.
#Path Questions
fading spindle
silent frigateBOT
pure thistle
Do you have any path questions where the starting point is the bottom left of so...
like a bunch of sqaures?
fading spindle
Yeah
pure thistle
Yeah
Alr! can you draw me a square composed of 4 small squares first?
We'll begin with that
fading spindle
Alr! can you draw me a square composed of 4 small squares first?
I'm eating rn, after i finish and wash up I'll do it.
pure thistle
I'm eating rn, after i finish and wash up I'll do it.
Alright!
dapper cloud
You can label each point with the number of paths to that point starting from the ones closest to the origin, and then use those labels when deciding the next labels.
For instance, starting from the top left and working our way down:
1 - 1 - 1 - 1
| | | |
1 - 2 - 3 - 4
| | | |
1 - 3 - 6 - 10
| | | |
1 - 4 - 10- 20
(where we get the 10 on the 4th row 3rd column because we can enter this cell either from the left, where there is a 6, or from the top, where there is a 4, for instance.)
Notice that this is related to Pascal's triangle, in the case where we have a rectangle.
@fading spindle hth!
fading spindle
You can label each point with the number of paths to that point starting from th...
I think this is called the junction method, its the only thing i know about these questions
it helped me with aimo today
pure thistle
Look at this cute diagram. Consider that you are only allowed to move right and up
is that okay?
fading spindle
Yeah
civic mantle
pure thistle
and you want to go from orange to purple
Consider moving right one square as "a"
and up as "b"
You'll noticed that the solution is basically the permutation of a a b b
is that okay so far?
@fading spindle
fading spindle
Yeah
pure thistle
Alr, can you find me the ways that you move from orange to purple?
only shorcuts, no backward moves
fading spindle
fading spindle
pure thistle
idk how to use perms and combs for nonsquares but i used junction
still, let's begin with drawing the graph
oh, fast
pure thistle
look, so here's the key.
You basically have to move 3 right move and 2 up move to reach the goal
right?
fading spindle
yeah
pure thistle
so what's the permutation of it
pure thistle
Consider moving right one square as "a"
and up as "b"
You'll noticed that the so...
according to this
fading spindle
5!/(2! . 3!)
fading spindle
yay
pure thistle
and in fact, omni's approach still works
civic mantle
fading spindle
fading spindle
How do I do paths with 3d shapes?
pure thistle
How do I do paths with 3d shapes?
Very good question.
Still, you apply the permutation concept here
For example, go left = a, go up = b, go forward = c
and find how many left/ up/ forward are there before reaching the goal
pure thistle
For example, in 3x2 grid, you need to go right three times and go up two times to reach the goal
fading spindle
w
pure thistle
Do you wanna learn more? or just call it a night
I can also teach you how to solve grids involving barricade(s)
fading spindle
I got some homework to do but I can do one more question or concept
pure thistle
I got some homework to do but I can do one more question or concept
Sure, draw me a 3x3 grid and draw a cross in the middle
fading spindle
pure thistle
no, draw a cross on a road intersection
fading spindle
Like this?
fading spindle
hmm
pure thistle
it's very difficult to exlcude the ways to reach the spot involving crossing that X
So therefore, generally speaking, we'd like to apply omni's approach here
and here's how you do it
civic mantle
fading spindle
oh u can still add it like triangular numbers
fading spindle
I haven't learnt binomial stuff yet so I haven't really looked at pascals triangle but i think through junction the sum of those two numbers being the top right number is a triangular number idk
pure thistle
I haven't learnt binomial stuff yet so I haven't really looked at pascals triang...
yeah, it might be tough to pick it up right now
fading spindle
Yeah
fading spindle
the competition im preparing for is yrs 7 to 10 following the australian schooling system
i did it today and although i think i got the paths question right i still did pretty bad
i do want to get invited to the next round next year though
pure thistle
you did fairly well honestly
pure thistle
i do want to get invited to the next round next year though
understandable
fading spindle
you did fairly well honestly
not enough for a high distinction ;-;
im gonna do my hw now
bye
fading spindle
alr
civic mantle
.close
silent frigateBOT
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