Skip to main content
Posts
Three ants are sitting at the three corners of an equilateral triangle.
Each ant starts randomly picks a direction and starts to move along the
edge of the triangle. What is the probability that none of the ants
collide?
'THIS' is the probability!
What was the problem?
Each ant can decide to go either clockwise or anti-clockwise. That is there are 2 options available for each ant to go. Hence, there will be total 2x2x2 = 8 possible combination of ants' different paths.
Now 2 ants won't collide if & only if all are either moving clockwise or anti-clockwise. In short, out of 8 possible combinations only 2 combinations are there where ants won't collide.
Hence, the probability that ant won't collide is 2/8 = 0.25.
A newspaper made of 16 large sheets of paper folded in half. The
newspaper has 64 pages altogether. The first sheet contains pages 1, 2,
63, 64.
If we pick up a sheet containing page number 45 what are the other pages that this sheet contains?
Here is the solution of puzzle!
What was the puzzle?
If the page starts with odd number 1 & back side followed by even 2 then at the back of page number 45, there must be number 46.
Generally, for the page p, page 65 - p shares the same sheet as p. Like page 1 and 65-1 =64, page 2 and 65-2=63 page are on the same sheet.
Therefore, page 45 must be on the same sheet as 65 - 45 = 20 page number. And the page 46 must be on the same sheet as page 65 - 46 = 19.
In short, the pages 19,20,45 and 46 must be on the same sheet.
Sara needs to trek from an oasis to a destination 10 miles away across a barren desert.
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!
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.
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).
Read the detective's logic in the case!
