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Andrea’s only timepiece is a clock that’s fixed to the wall. One day she forgets to wind it and it stops.
She travels across town to have dinner with a friend whose own clock is always correct. When she returns home, she makes a simple calculation and sets her own clock accurately.
How does she manage this without knowing the travel time between her house and her friend’s?
That's how she manages to set it accurately!
How it was mistimed?
Andrea winds her clock & sets it to the arbitrary time. Then, she leaves her house and when she reaches her friend's house, she note down the correct time accurately. Now, after having dinner, she notes down the correct time once again before leaving her friend's house.
After returning to home, she finds her own clock acted as 'timer' for her entire trip. It has counted time that she needed to reach her friend's house + time that she spent at her friend's house + time she needed to return back to home.
Since, Andrea had noted timings at which she reached & left her friend's house, she can calculate the time she spent at her friend's house. After subtracting this time duration from her unique timer count she gets the time she needed to reach to & return from her friend's house.
She must have taken the same time to travel from her home to her friend's home and her friend's home to her home. So dividing the count after subtracting 'stay time' she can get how much time she needed to return back to home.
Since, she had noted correct time when she left her friend's home, now by adding time that she needed to return back to home to that, she sets her own clock accurately with correct time.
Let's try to understand it with example.
Suppose she sets her own clock at 12:00 o' clock and leave her house. Suppose she reaches her friend's home and note down the correct time as 3:00 PM. After having dinner she leaves friend's home at 4:00 PM.
After returning back to home she finds her own clock showing say 2:00 PM. That means, she spent 120 minutes outside her home with includes time of travel to and from friends home along with time for which she spent with her friend. If time of stay at her friend is subtracted from above count, then it's clear that she needed 60 minutes to travel to & return back from friend's home.
That is, she needed 30 minutes for travel the distance between 2 homes. Since, she had noted correct time as 3:00 PM when she left friend's home, she can set her own clock accurately at 3:30 PM.
I place four balls in a hat: a blue one, a white one, and two red ones.
Now I draw two balls, look at them, and announce that at least one of
them is red. What is the chance that the other is red?
Well, it's not 1/3!
What was the puzzle?
It's not 1/3. It would have been 1/3 if I had taken first ball out, announced it as red and then taken second ball out. But I have taken pair of ball out. So, there are 6 possible combinations.
red 1 - red 2
red 1 - white
red 2 - white
red 1 - blue
red 2 - blue
white - blue
Out of those 6, last is invalid as I already announced the first ball is red. That leaves only 5 valid combinations.
And out of 5 possible combinations only first has desired outcome i.e. both are red balls.
Hence, there is 1/5 the chance that the other is red
Okay, I’ll ask three questions, and if you miss one I get your house. Fair enough? Here we go:
1.A clock strikes six in 5 seconds. How long does it take to strike twelve?
2.A bottle and its cork together cost $1.10. The bottle costs a dollar more than the cork. How much does the bottle cost?
3.A train leaves New York for Chicago at 90 mph. At the same time, a bus leaves Chicago for New York at 50 mph. Which is farther from New York when they meet?
You need little common sense in answering above!
What where questions?
1. A clock strikes six in 5 seconds. How long does it take to strike twelve?
A: Not 10 seconds, it takes 11 seconds.
Here, interval between 2 strikes is 1 second i.e. if counter started at first strike, it will count 1 second after second strike, 2 seconds after third strike & so on.
Hence, 11 seconds needed for strike 12.
2.A bottle and its cork together cost $1.10. The bottle costs a dollar more than the cork. How much does the bottle cost?
A: Not 1 dollar, it would cost $1.05.
If x is cost of cork,
x + (x +1) = 1.10
2x = 0.10
x = 0.05
Hence cost of bottle is $1.05 and cost of cork is $0.05
3.A train leaves New York for Chicago at 90 mph. At the same time, a bus leaves Chicago for New York at 50 mph. Which is farther from New York when they meet?
A: Obviously, when they meet at some point then that point must be at the some distance from New York. Hence, they are at the same distance from the city.
The diagram below shows 40 matchsticks arranged in a square grid.
What is the fewest number of matchsticks that need to be removed so that there are no squares (of any size) remaining?
This is how it can be done!
