The most beautiful math problems are practical, give an impression that the problem cannot be solved, and finish by an unexpected (surprise) solution. Seven famous math word problems suggested by Martin Gardner, Anatole Lucas, Euler, Vladimir Arnold and Monty Hall challenge adults and kids.

1. Best Math Problems
© Igor Kokcharov

2. challenging
surprising
practical

3. Three sailors come across a pile of coconuts. The
first sailor takes half of them plus half a coconut.
The second sailor takes half of what is left, plus
half a coconut. The third sailor also takes half of
what remains, plus half a coconut. Left over is
exactly one coconut, which they toss to a monkey.
How many coconuts were in the original pile?
1. Martin Gardner’s favorite problem

4. In a city, there was a tradition to walk and cross
over each of the city bridges only once. If a
person starts and finishes at the same point, can
he accomplish this task?
Can you form a general rule when it it possible?
2. Euler bridge problem

5. 3. Morozkin’s problem told by V. Arnold
Two old women started at sunrise and each
walked at a constant different velocity. One went
from A to B and the other from B to A. They met
at noon and, continuing with no stop, arrived
respectively at B at 4 p.m. and at A at 9 p.m.
At what time was the sunrise on this day?

6. Every day at noon, a ship leave Le Havre for New
York and another ship leaves New York for Le Havre.
The trip lasts 7 days and 7 nights. How many ships
will a ship leaving Le Havre meet at sea?
4. Lucas problem

7. A manager wants to hire an assistant. Once
rejected, an applicant cannot be recalled. He
interviews N randomly chosen people out of 100
applicants, rejects them and records the best
score S. After that, he interviews others and stops
when the person has a score better than S. What
number N do you recommend to the cruel man?
5. Secretary problem

8. A rich man will invest in only one of 3 companies:
A, B, or C. I will make a lot of money if I invest in
the same company; otherwise I am a bankrupt. I
decide to invest in company A and I inform the
man. He assures me that he does not invest in
company C. What company do you recommend
for me to make the investment?
6. Monty Hall’s challenge

9. Queen Dido and her followers arrived in North
Africa. The locals told them that they could have
the coastal area that an ox hide would cover. She
cut the hide into a series of thin strips, jointed
them together, and formed a coastal shape. If
you had a long strip, which shape would you
choose to maximize the enclosed area?
7. Legend of Carthage

10. 1. http://www.aplusclick.com/t.htm?q=3713
2. http://www.aplusclick.com/t.htm?q=2153
3. http://www.aplusclick.com/t.htm?q=3753
4. http://www.aplusclick.com/t.htm?q=3744
5. http://www.aplusclick.com/t.htm?q=2213
6. http://www.aplusclick.com/t.htm?q=2180
7. http://www.aplusclick.com/t.htm?q=2100
Answers

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