Problems for summer time - Part 1

1. 5 friends and handshakes

5 friends exchanged 4 handshakes with each other. How many handshakes they did?

Answer: 40

2. Fake coin

There are 9 coins and one of them is fake. We know that the fake coin is lighter than others. How to determine which coin is fake with 2 attempts?

Answer: Divide 9 coins into 3 sets with 3 coins in each set. Compare 2 sets. If one set is lighter than the other then it means that the fake coin in the lighter set. If those two sets weight is the same then the fake coin in the third set. Now we know that the fake coin among 3 coins. Select 2 coins from those 3 coins and compare them. If one is lighter then that would be the fake coin. If they are equal then the third coin is fake.

3. Continue the sequence

Here is the sequence: 2, 20, 40, 400, 800. Could you please continue it?

Answer: The second number is 10 times more then the first. The third number is twice as much as second, the fourth is 10 times more than the third, the fifth is twice as much as the fourth
2, 20, 40, 400, 800, 8000, 16000, ...

4. Interesting square

Imagine the square 3 x 3 (9 cells all together). Put numbers from 1 to 9 in such a way that one number should be in one cell, a number is not repeated, sum of the numbers that reside on the same level horizontally, vertically, and diagonally is the same.

Answer:
One of the answers
2 7 6
9 5 1
4 3 8

5. Cleaning windows

6 workers clean 6 windows within 6 minutes. What is the minimal number of workers needed to clean 100 windows within 100 minutes?

Answer: 6

6. Treasure hunters

2 treasure hunters found treasure. They don't have any means to measure that. How to divide the treasure between those two treasure hunters in most fair fashion?

Answer:
One treasure hunter divides treasure in the way he/she thinks fair and the other one chooses the part he/she likes.

7. Saturday

September 1 2001 was Saturday. What day of the week was October 1 2001?

Answer: Monday

8. Kids in circle

There is some number of kids stay in circle. We know that the third person on the left from James is the same person who is 11th on the left from James. How many are in the circle?

Answer: 8 or 4 or 2

9. Third grade

On Tuesday there are 4 classes in the third grade: Math, Writing, Reading, and Arts. How many different combinations (in what order they go) exist?

Answer: 24

10. Cats competition

2 cats participate in running competition. They need to run first from point A to point B and then back from point B to point A. The first cat is running with the same speed the whole distance. The second cat is running twice as fast than the first one from point A to point B , but from point B to point A the first cat is running twice as fast as the second cat.
Who will finish first?

Answer: First cat