Stairway to Heaven

Probability Level 3

How many ways can we spell out H-E-A-V-E-N, if each time we can only move to the right, and have to stay at the same vertical height or higher?

Note: When you go up higher, you can go to any higher level. As an explicit example, from the bottom-most A, you can go to any of the V's, so there are 3 possibilities.


The answer is 132.

Chung Kevin by Chung Kevin , 45, Australia

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1 solution

Ossama Ismail
Feb 7, 2017

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Oh yes! That's very similar to what I did to determine the answer at the start.

I realized that the sequence 1, 2, 5, 14, 42, 132 corresponds to the catalan numbers .

If you "rotate the image 13 5 ∘ 135^\circ anticlockwise, we can see the bijection.

Chung Kevin - 4 years, 4 months ago

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