Problems

Seven nines written out in a series: 9 9 9 9 9 9 9. Put some “\(+\)” or “\(-\)” between some of them, so that the resultant expression equals 1989.

The tower clock chimes three times in 12 seconds. How long will six chimes last?

1. A bagel is cut into sectors. Ten cuts were made. How many pieces did this make?

2. Woodchucks are sawing a log. They made 10 cuts. How many pieces were made? How can we explain why the answers in the previous two questions are different?

Are the sum and product odd or even for:

a) two even numbers?

b) two odd numbers?

c) an odd and an even number?

In a purse, there are 2 coins which make a total of 15 pence. One of them is not a five pence coin. What kind of coins are these?

15 points are placed inside a \(4 \times 4\) square. Prove that it is possible to cut a unit square out of the \(4 \times 4\) square that does not contain any points.

On an island, there are knights who always tell the truth, and liars who always lie. What question would you need to ask the islander to find out if he has a crocodile at home?

What is there a greater number of: cats, except for those cats that are not named Fluffy, or animals named Fluffy, except for those that are not cats?

Five oaks are planted along two linear park alleys in such a way that there are three oaks along each alley, see picture. Where should we plant the sixth oak so that it will be possible to lay two more linear alleys, along each of which there would also be three oak trees growing?

The smell of a flowering lavender plant diffuses through a radius of 20 m around it. How many lavender plants must be planted along a straight 400m path so that the smell of the lavender reaches every point on the path.