Path Counting Brain Teaser

[ilkhamharzmiy]

do you know path algebra and its representation?? if yes, then put some video please!!

[midnight4fox]

what program are you using?

[Garrett666999]

Come teach at my highschool? (:

[radius34]

just go six any side then go to the last mark peroid~!!!!

[NewScienceAu]

This one I liked! Cool! I've got it right a way!

[ProGroupRacingAU]

This is the easiest one o far! Had fun, anyway!

[valdas0]

I saw this on Arts of problem solving so I already knew that I had to use combinatorics.

[efrestein]

10! / (5!*5!) easy :)

[AllisonMY]

i saw 11 ways

[gfaithw]

minesweeper.

[4NG3LxD3M0N]

id like you as a math teacher this is actually fun o.o;

[francis0000b]

@LemonyDragon yeah, i recognized how to solve it by pascal's triangle at 0:47

[denni0302]

soon as he drew the star i thought pascals triangle :D didnt pause it to find out how many ways there were, just skipped to end and saw it was pascals three cornered friend

[UltraMaXAtAXX]

Pascal's triangle. MIND = BLOWN.

[kinovers4]

10C5

[povrick]

Thank you so much for such a well spoken and demonstrated explanation of this concept. This has helped me no end. Who would have thought youtube could be used for something other then videos of cute cats and charlie biting his brothers finger. Thank you again, i will check out your other vids

[hctivas]

this is basically dynamic programming.

[TheGozzila]

COOOL

[Pyrobladestudiosx1]

Holy schamoly it looks like pascal's triangle!

[SkInNyT3]

huh? i dont even know what the quistion is!

[DartmouthAlum96]

This is beautiful!

[rhysy07]

HEAPS OF combinations is all i say

[nhojmabon]

Here's how I solved it:

You will need to make 5 steps down and 5 steps to the right.

R - Right, D - Down

One combination is 'RRRRRDDDDD', another is 'DRRRRRDDDD'. Finding all combinations of this 10 lettered word is a standard high school math problem.

Possible combinations = (Total letters factorial)/(5D's factorial x 5R's factorial) = 10(fac)/(5fac x 5fac) = 10x9x8x7x6x5x4x3x2x1/(5x4x3x2x­1 x 5x4x3x2x1) = 252 combinations.

[Michel290389]

Wow, that's a cool solution!

I haven't even thought about using combinatorics at this problem...

[ocram3333]

@nhojmabon darn you! I was just going to write a comment saying that exactly. But I guess I´m 1 year late, hahaha! Nice to see someone else thought about it the same way though.

[nhojmabon]

@ocram3333 hehehe sorry about that, better luck next time.

[dheeraj54]

@nhojmabon nice method

mine was stupider

he has to walk 10 steps he has to select any 5 to the right and the rest automatically become upward

so the answer is 10c5 or 10 choose 5 =10!/5!.5!

[nhojmabon]

@dheeraj54 Nice method, definitely not stupider.

[dheeraj54]

@nhojmabon thanks

[Raysyns]

This was a pretty cool problem, I got it with solving small squares and looking for a pattern. I got it in the form of a sum as well, so you get c(n-2+k,k) from k=0 to n-2, where n is the dimensions. Never seen it before. Was cool to see how it worked once I realised it was using the binomial theorem.

[Raysyns]

oh and the sum is times 2 which I forgot to put

[02280228]

lol at first I thought there were 12 ways. Now after the video I know i couldn't be more wrong. To see the connection to the binomial coefficients amazed me!

Thank you Sal for making these videos!!!!

[y2knoproblem]

36 ways

[konopong]

Instead of going from cell to cell, if you go from vertex to vertex (following the line segments) I came up with 924 paths. Technique is the same. These problems are great. Thanks!

[veers0r]

Pascals triangle :)

[MrMss4]

You have to go down 5 times and right 5 times, for a total of 10 moves. We can put 5 "down-moves" in those 10 moves C(10,5) ways, and count the rest as right-moves.

Notice this works in rectangular formations as well, regardless of whether you pick downmoves or rightmoves to work with as C(n, n-r) always equals C(n, r).

[blacksilkblacksilk]

That was fun to watch and inspiring.

Also very good explaining and didactic built up.

have a nice day

silk

[Lexiathan]

Wow, I did not notice the connection with binomial coefficients at first, but it will be a very useful concept to have. Even though the grid problem was easy, I am glad you uploaded the video.

[cconrad246]

10! / (5! x 5!)

[doctish]

Pythagorean ?

[undeadxazn]

Pascal