### Brain Teasers

# Shadow's Adventure

Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

Shadow the Adventurer can't get enough of adventures. So he decides to embark on a great adventure. This is his adventure map.

...................4a - 5a - 6a - HOME

.....2a - 3a - 4b - 5b - 6b - HOME

1 - 2b - 3b - 4c - 5c - 6c - HOME

.....2c - 3c - 4d - 5d - 6d - HOME

..................4e - 5e - 6e - HOME

His main intention is to start from point 1, go to point 6c and go home. He may only move one space on the map at a time. He may not go backwards, or up and down. So from point 1, he might go to 2a, then to 3b, then to 4d and so on. When he reaches points 6a, 6b, 6c, 6d or 6e, he can take a long route, or a short route home.

What is the probability of Shadow reaching point 6c and taking the short route home?

...................4a - 5a - 6a - HOME

.....2a - 3a - 4b - 5b - 6b - HOME

1 - 2b - 3b - 4c - 5c - 6c - HOME

.....2c - 3c - 4d - 5d - 6d - HOME

..................4e - 5e - 6e - HOME

His main intention is to start from point 1, go to point 6c and go home. He may only move one space on the map at a time. He may not go backwards, or up and down. So from point 1, he might go to 2a, then to 3b, then to 4d and so on. When he reaches points 6a, 6b, 6c, 6d or 6e, he can take a long route, or a short route home.

What is the probability of Shadow reaching point 6c and taking the short route home?

### Answer

45/326. There are 326 possible routes Shadow can take from point 1 to Home. Only 90 of these routes take him to point 6c, where he may take the long route or short route home, so 90/2=45. So 45/326.Point 6a = 42 routes

Point 6b = 76 routes

Point 6c = 90 routes

Point 6d = 76 routes

Point 6e = 42 routes

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