



Speedy Sums
 
 

A salesman drives from Amsterdam to The Hague.
The first half of the distance of his journey, he drives at a constant speed of 80 km/h.
The second half of the distance of his journey, he drives at a constant speed of 120 km/h.
 

The Question:
What is the salesman's average speed for the complete journey?
 

A Hint :
The solution is not 100 km/h!
 

The Answer:
Click here!...
 

Another Question:
A racecar driver drove, on a 4 km long racecourse, at an average speed of 120 km/h for the first 2 km.
How fast does he have to go the second 2 km to average 240 km/h for the entire course?
 

Another Answer:
Click here!...
 

Yet Another Question:
Makkum and Stavoren are two villages.
Michael and Donald want to go from Makkum to Stavoren.
They leave at the same time.
Michael goes by bicycle.
Donald goes by car, which is six times as fast as Michael is on his bicycle.
Unfortunately, Donald has a car breakdown halfway between Makkum and Stavoren.
Fortunately, a passing farmer gives him a lift to Stavoren on his tractor.
Unfortunately, the farmer drives only half as fast as Michael drives on his bicycle.
Who of the two arrives first in Stavoren?
 

Yet Another Answer:
Click here!...
 

The Fourth Question:
Normally, the train between Utrecht and Amersfoort drives at an average speed of 90 km/h.
One day, the train was delayed a little.
Because of this, the average speed of the train between Utrecht and Amersfoort was only 70 km/h,
and the train arrived four minutes late in Amersfoort.
What is the distance between the stations of Utrecht and Amersfoort?
 

The Fourth Answer:
Click here!...
 

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The Prince and the Pearls
 
 

Long ago, a young Chinese prince wanted to marry a Mandarin's daughter.
The Mandarin decided to test the prince.
He gave the prince two empty, porcelain vases, 100 white pearls, and 100 black pearls.
"You must put all the pearls in the vases", he told the prince.
"After this, I will call my daughter from the room next door.
She will take a random pearl from one of the two vases.
If this pearl is a black one, you are allowed to marry my daughter."
 

The Question:
What was the best way in which the prince could divide the pearls over the vases?
 

The Answer:
Click here!...
 

Another Question:
You have three vases:
one vase containing two white pearls,
one vase containing one white and one black pearl,
and one vase containing two black pearls.
From one of these vases, a pearl is taken.
This pearl turns out to be white.
What is the probability that the other pearl in the same vase is also white?
 

Another Answer:
Click here!...
 

Yet Another Question:
You have ten vases.
Five of the vases contain a white pearl and four of the vases contain a black pearl
(note that a vase may contain both a white and a black pearl!).
You randomly select one of the ten vases.
What is the probability that the vase you chose is empty?
 

Yet Another Answer:
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Palindrome Puzzle
 

A number is called a palindrome when it is equal to the number you get when all its digits are reversed.
For example, 2772 is a palindrome.
We discovered a curious thing. We took the number 461,
reversed the digits, giving the number 164, and calculated the sum of these two numbers:
461
164 +

625
We repeated the process of reversing the digits and calculating the sum two more times:
625
526 +

1151
1511 +

2662
To our surprise, the result 2662 was a palindrome.
We decided to see if this was a pure coincidence or not.
So we took another 3digit number, reversed it,
which gave a larger number, and added the two.
The result was not a palindrome.
We repeated the process, which resulted in another 3digit number that was still not a palindrome.
We had to repeat the process twice more to arrive at a 4digit number, which was a palindrome finally.
 

The Question:
What was the 3digit number we started with the second time?
 

The Answer:
Click here!...
 

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