INTERESTING MATHEMATICS

Square pond and 4 oaks• We have a square pond, the 4 oaks are growing at the corners of this pond.

• You should increase the area of the pond twice, but the oaks have to stay in their places and the pond has to stay square.

Who is the first - cat or dog?• The cat-sprinter moves using jumps which are two meters long each, and the dog-sprinter moves using jumps which are three meters long. The dog can jump twice while the cat can jump three times. The distance they have to cover is 100 meters long. Who will come first?

Can you solve it?

• What number is missing?• 111=13• 112=24• 113=35• 114=46• 115=57• 117=???

Moneymaking choice

You are invited to work as a financial analyst at Google. They promise a starting salary of $ 100 000 per year and two options to increase it:

• 1.Your salary will be increased for $ 15 000 once a year• 2. Your salary will be increased for $ 5000 every six months.

Which choice do you think is more moneymaking?

Seamstress

A tailor has a piece of cloth(18 m long) and every day she cuts off 3 meters. When will she cut the last piece?

Basket with an apple• There are 5 apples in the basket. Can we share them equally among 5 friends so, that 1 apple will stay in the basket?

Broken window• 9 pupils were staying in the class during

the break. One of them broke the window. When the teacher asked the pupil, they said:

• Peter: Dmytro has done it..• Stas: It is not true.• Maria: I have broken it.• Stephen: Mary or Anne have broken the

window.• Dmitry: Stas is lying.• Andrew: It was Mary.• Sasha: No, Mary hasn’t broken the window.• Anna: Mary and I haven’t done it.• Marina: Anna is right, but Dmytro hasn’t

done it either.

2 or 10

• When do we look at number 2 but say 10?

The following letters

• What are the next letters in this line:• M,V,E,M,J…

Fast fly• Two cities A and B, are located at the distance of 30 km from each other. From both of these cities two men start off towards each other and walk without stopping, their speed is 5 km per hour. At the same time a fly starts flying from city A with the speed of 10 miles per hour. The fly overtakes the first man and reaches the other one who is walking from city B. When they meet, the fly immediately turns back and flies to the first man. When the fly reaches the first man, it immediately flies back to the second man, and so it continues flying until two men finally meet. Then it calms down and sits on one man’s hat. How many kilometers has the fly covered?

Sum or product• What is bigger, the sum of all numbers or their product?

Greedy receptionist• Three musicians-travelers booked a three-room suite at a hotel which cost $30. Every musician paid $10. Then it turned out that the suite cost only $25. So the receptionist went to the musicians’ room to give back their $5. By the way, he realized that it’s difficult to divide $5 among three persons. So he decided to put $2 in his pocket and gave every person $1 and suddenly he made a discovery. Each musician paid $9, and together they spent 9 × 3 = 27 dollars. Two dollars the receptionist had in his pocket. So staying at the hotel cost $29 for the musicians. And where had the thirtieth gone? This question worried the receptionist so much that he returned the musicians the hidden two dollars, and they explained why he had no reason to worry. What did the musicians say?...