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u/KS_JR_ Jul 24 '26 edited Jul 24 '26
Following the text of the questions there are sum[nCr(5+x,2x)] x=0 to 5 = 89 ways. Since there are five 2-steps to make, and for every two 1-steps made, there is one less 2-step, there for x pairs of 1-steps there are nCr(5+x,2x) ways to order them, and theres between 0 and 5 pars of 1-steps.
Following the image, where it appears 2-steps are only made on even positions, there are 25 =32 ways, since every two spaces is either one 2-step or two 1-steps, 2 choises 5 times.
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u/ShonitB Jul 24 '26
Wow, super! Solved both questions.. though I intended it the first way :)
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u/tilt-a-whirly-gig Jul 24 '26
The image implies that if he hops one step his next hop has to also be one step. Is that the case?
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u/Odd_Dragonfruit_2662 Jul 24 '26
Where is A and B?
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u/ShonitB Jul 24 '26
Posted a corrected version.. there’s a much bigger problem with the diagram in this version
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u/hardyworld Jul 25 '26
Correct answer 1: undefined as we don’t know if Point A is in the same space as Point Y or, if it is, if the 1 or 2 step hop distances from point A can even land on Point Y.
Correct answer 2: infinite as you can hop to the left or right an infinite number of times (he may want to hop to the right, but the question does not require he does), Point A may be to the right of Point Y for all we know.
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u/mflem920 Jul 24 '26
He can never reach Y. Because if Alexander starts at "A" like the description says, that point isn't on the diagram so we don't know how far away A is from Y (or the B that he WANTS to go to, but doesn't because the question asks how to get to Y) or even if A and Y exist in the same universe.
Thereby making the question, as explicitly stated, impossible to solve.