# Possibility question; isn't the answer 2?

• x86
In summary, the conversation was about a math question on the website aplusclick. The question asked how many ways a boy could get to a point 8 kilometers north and 8 kilometers east of his starting point, with the condition that he never walks in the same direction. The answer was initially given as 2^8 or 256, but it was discussed that the answer should actually be 2. The conversation then delved into different interpretations of the question and how it could lead to different answers. Ultimately, it was concluded that the answer could be 256 if the restriction on walking directions was removed, but the correct answer with the given conditions was 2. The conversation ended with a humorous note about exploring different aspects of a

#### x86

So I'm doing some math stuff on this internet website for fun, aplusclick. Anyway, there was this question on the site:

"A boy begins walking from his starting point. Each hour, he either walks one kilometer to the east or one kilometer to the north, but he never walks in the same direction.

In how many different ways can he get to a point that is 8 kilometers to the north and 8 kilometers to the east of his starting point?"

The answer is 2^8, or 256. But shouldn't it be 2?

He can either start by going east, then north, then east - until his displacement is 8 km N, 8 km E
or he can start by going north, then east, then north, etc

So shouldn't it be 2? Can someone break this down for me if I am wrong?

You are correct - the question is poorly worded: what question does the answer belong to?

Yeah, for the answer to be 256, you have to remove the restriction that he never walks the same way for two consecutive 1KM legs.

phinds said:
Yeah, for the answer to be 256, you have to remove the restriction that he never walks the same way for two consecutive 1KM legs.

But then the answer is 16!/(8!8!) =12870

To get 256, he has to walk for 8 hours, without a restriction on walking directions.

An alternative interpretation: He never deviates more than 1km north or east from the direct (diagonal) path, so the difference between "hours moved north" and "hours moved east" is at least -1 and at most 1. That would give 256 as well.

You know, most people would have responded to the question as x86 did and leave it at that.
I sometimes wonder if we, who go explore things like which question the answer belongs to are just plain weird.
Mind you - it more fun this way :)

## 1. What is a possibility question?

A possibility question is a type of question that asks about the likelihood or feasibility of something happening or being true.

## 2. How is a possibility question different from other types of questions?

Possibility questions are different from other types of questions, such as factual or opinion questions, because they focus on the potential for something to happen or be true rather than seeking a specific answer.

## 3. Can a possibility question have a definitive answer?

No, a possibility question does not have a definitive answer. It is meant to generate discussion and explore different perspectives on the likelihood of something happening or being true.

## 4. Why is the answer to a possibility question often subjective?

The answer to a possibility question is often subjective because it depends on individual beliefs, opinions, and experiences. What may seem possible to one person may not seem possible to another.

## 5. How can scientists use possibility questions in their research?

Scientists can use possibility questions in their research to explore potential outcomes or solutions, assess the feasibility of a hypothesis, or consider alternative explanations for their findings. Possibility questions can also inspire new research and spark critical thinking in the scientific community.