Best Math Problems

© Igor Kokcharov

challenging surprising

practical

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

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

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?

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

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

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

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

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