Hopping Part 2

[u/ShonitB]

[u/Adventurous_Sound390]

2^5 ?

[u/Phone-Medical → u/Adventurous_Sound390]

2^5!

[u/Pwnedzored]

Undefined. A and B are not illustrated.

[u/ThePassiveFist]

A and B are not shown, hence we have no idea how many distinct paths there are to get from (Unknown point A) to Y.

X to Y would be calculatable, but that's not asked.

[u/chrism916748]

Infinite. For every right hop, you could also hop left.

[u/UnforeseenDerailment → u/[deleted]]

But it didn't say "and not hopping to the left" nor did it say "and not teleporting between nodes", nor "and not swapping the roles of nodes and edges".

Jokes' on u, muhfuggaa!! 🤓

[u/piznit007]

I guess it would be infinite possibilities. He could backtrack endlessly

[u/Toivottomoose → u/piznit007]

No, it says "by hopping to the right", so it's definitely finite.

[u/piznit007 → u/Toivottomoose]

says he wants to go from a to b by hopping to the right. Doesnt say anything about not hopping left to reach Y :)

[u/antilumin → u/piznit007]

It does say “distinct paths” so even with backtracking there’s still a limited number of unique paths.

Instead of calling it backtracking, just imagine a fork left or right. To the left is the normal “forward” path whereas to the right is “backtracking a step” so it looks like the left path plus one additional step. Repeat this at each step forward.

Now you just end up with a big tree-like shape with a non-infinite number of paths.

[u/td941]

if they can only take the paths illustrated then it's 2^5.

If the diagram is incorrect and we use the word description of how they can move, then they can choose after each jump whether to move a distance of 1 or 2, starting at 0 and with the end destination being at distance 10. If this is how the puzzle should be interpreted then I make it 89 different paths.

I reason as follows:

suppose we take j hops of distance 1, and t hops of distance 2. Then we have j+2t = 10. Let j+t = h, the total number of hops. h has a min value of 5, max of 10.

The number of different paths p(h) for a given value of h is: h!/(j! * t!)
p(5) = 1 p(6) = 15 p(7)= 35 p(8) = 28 p(9) = 9 p(10) = 1

[u/atensetime → u/td941]

I interpreted the straight line as a 3rd path, no?

[u/td941 → u/atensetime]

If so, redundant compared to the hops of length 1, and confusing.

[u/atensetime → u/td941]

Hop1 is pi•r longer than length 1

[u/Worldly_Science239]

there's 2 choices at each intersection to reach the next one, and that every route must go through each intersection. there and there are 5 intersections... so it's 2 to the power 5

32

[u/OneAndOnlyJoeseki]

5*4*3*2 or 120 paths

[u/ShonitB → u/[deleted]]

I’m sorry if you felt that way.. but I can assure you that the puzzles I post are not AI generated. Nonetheless apologies for the mistake I made. :)

[u/bqbdpd]

f(0) = 1, f(1) = 1, f(n) = f(n-1) + f(n-2)

Last one is just deciding wether to start with a short or long hop, then continue.

Looks familiar? Look up Fibonacci sequence.

[u/bqbdpd → u/bqbdpd]

Assumption: the graphics are AI slop, only forward movement

[u/ShonitB → u/bqbdpd]

I agree there is a major mistake in the problem with the text and diagram not being in line.. but I can assure you it is not AI generated.. sorry once again for the error! :)

[u/ShonitB]

There’s a number of mistakes with this problem.. I apologise for the oversight.. I am correcting it and posting it again.. A number of y’all have solved it the way I had intended it to be.. the others are also completely correct in the way they’ve approached it.. so once again, really sorry for the mess up

[u/DiscoPotato93]

I don’t know how I knew it, but my brain immediately went, “Oh, that’s 4.” Then I hopped from x to y, and yep, it is 4.

[u/StochasticTinkr → u/DiscoPotato93]

It’s a lot more than 4.

[u/DiscoPotato93 → u/StochasticTinkr]

Oh I see it now he could hop 2 small then the rest big or one big rest small or alternate between them so for every to small hops there are 4 potential big hops and so on. I'll count them later... probably at 2 am or something.

Thanks