Miracle Mountain

Braingle.com on Oct 27, 2024

By clicking submit, I authorize Arcamax and its affiliates to: (1) use, sell, and share my information for marketing purposes, including cross-context behavioral advertising, as described in our Privacy Policy , (2) add to information that I provide with other information like interests inferred from web page views, or data lawfully obtained from data brokers, such as past purchase or location data, or publicly available data, (3) contact me or enable others to contact me by email or other means with offers for different types of goods and services, and (4) retain my information while I am engaging with marketing messages that I receive and for a reasonable amount of time thereafter. I understand I can opt out at any time through an email that I receive, or by clicking here

A hiker climbs all day up a steep mountain path and arrives at the mountain top where he camps overnight. The next day he begins the descent down the same trail to the bottom of the mountain when suddenly he looks at his watch and exclaims, "That is amazing! I was at this very same spot at exactly the same time of day yesterday on my way up."

What is the probability that a hiker will be at exactly the same spot on the mountain at the same time of day on his return trip, as he was on the previous day's hike up the mountain? Is the probability closest to (A) 99% or (B) 50% or (C) 0.1% ?

Solution:

The answer is (A). Since it must happen, the probability is actually 1 (100%).

Explanation: Firstly, consider 2 men, one starting from the top of the mountain and hiking down while the other starts at the bottom and hikes up. At some time in the day, they will cross over. In other words they will be at the same place at the same time of day.

Now consider our man who has walked up on one day and begins the descent the next day. Imagine there is someone (a second person) shadowing his exact movements from the day before. When he meets his shadower (it must happen) it will be the exact place that he was the day before and of course they are both at this spot at the same time.

Contrary to our common sense which seems to say that this is an extremely unlikely event, it is a certainty.

NOTE: There is one unlikely event here, and that is that he will notice the time when he is at the correct location on both days, but that was not what the questions asked.

Today's brain teaser courtesy of Braingle.com.