Friday, August 23, 2019

Sara's Desert Trek

Sara needs to trek from an oasis to a destination 10 miles away across a barren desert. 

Sara's Desert Trek

The facts:

  • Crossing one mile of desert requires using 1 gallon of water.
  • Sara can only carry 6 gallons of water at a time.
  • Sara can drop a water cache (of any amount of water from the supply she is carrying at that moment) at any of the nine stops along the route, and then pick up any part of the cache on a later trip.
What's the minimum number of times Sara must leave the oasis in order to cross the entire 10 mile span of desert?

This is how she optimizes her journey! 

Sara's Planning in Desert Trek

What was the challenge in journey?

1. First Sara collects 12 gallons of water at milepost 1 after having 3 trips from source. She uses 2 gallons (out of 6) for forward & backward journey from source to milepost & dropping 4 gallons in cache at milepost 1.

2.She collect 6 gallons more water at the start of 4th trip from source & drops 5 gallons at milepost 1. Now, she doesn't need to return back to source and 17 gallons of water available at milepost 1.

3.In next 2 rounds, she moves 8 gallons of water from milepost 1 to milepost 2 (1 for forward + 4 for drop + 1 for backward journey in each round). 

4.Now only 5 gallons left at milepost 2. She uses 1 gallon for journey from milepost 1 to milepost 2 and drop remaining 4 gallons at milepost 2. Now, 12 gallons of water is available at milepost 2.

3.Next, using 2 gallons (out of 6 which is maximum she can carry) she moves from milepost 2 to milepost 4 and drop 2 gallons at milepost 4 & comes back at milepost 2 using remaining 2. 

4. Again, on arriving back at milepost 2, she has left with 6 gallons of water at milepost 2 out of which she uses 2 to reach milepost 4 where 2 gallons of water still available there already collected in previous round. Now, she doesn't need to return back from
milepost 4.

5. She uses the remaining 6 gallons of water to reach at the milepost 10.

To conclude, Sara has to leave Oasis only 4 times as describe in steps 1 and 2 if she want to cross the entire 10 mile span of desert.  

Sara's Planning in Desert Trek

Wednesday, August 21, 2019

Murder or Suicide? - What Do You Think?

A dead body lies at the bottom of a multistory building. It looks as though he committed suicide by jumping from one of the floors.

When the detective arrives, he goes to the first floor of the building, opens the closed window, and flips a coin towards the floor. He goes to the second floor and does the exact same thing. He continues to do this until he gets to the top floor of the building.

When he comes back down, he states that it was a murder and not a suicide. How does he know that?

(Entry to the terrace was banned due to some ongoing work).

Murder or Suicide? - What Do You Think?

Read the detective's logic in the case!

Detective's Logic in Murder Mystery

What is the case?

Obviously, the person can't jump with window closed or come outside of the window & close that window from inside.

The detective checks if windows is closed from inside by opening window & flipping the coin toward the floor. He flips the coin to mark the count of that particular floor where window was closed from inside & he has to open it to flip the coin.

At the end, he collects as many coin as floors of that building. So he concludes that no floor had open window from where the person might have jumped.

Detective's Logic in Murder Mystery


So, he concludes that it was the murder and not the suicide.