There is a rectangular table. Two players start in turn to place on it one pound coin each, so that these coins do not overlap one another. The player who cannot make a move loses. Who will win with the correct strategy?
a) Two players play in the following game: on the table there are 7 two pound coins and 7 one pound coins. In a turn it is allowed to take coins worth no more than three pounds. The one who takes the last coin wins. Who will win with the correct strategy?
b) The same question, if there are 12 one pound and 12 two pound coins.
a) Prove that in any football team there are two players who were born on the same day of the week.
b) Prove that in the population of London, which is almost 9 million, there will be ten thousand people who celebrate their birthday on the same day.
On Easter Island, people ask each other questions, to which only “yes” or “no” can be answered. In this case, each of them belongs exactly to one of the tribes either A or B. People from tribe A ask only those questions to which the correct answer is “yes”, and from tribe B – those questions to which the correct answer is “no.” In one house lived a couple Ethan and Violet Russell. When Inspector Krugg approached the house, the owner met him on the doorstep with the words: “Tell me, do Violet and I belong to tribe B?”. The inspector thought and gave the right answer. What was the right answer?
Gerard says: the day before yesterday I was 10 years old, and next year I will turn 13. Can this be?
A toddler has \(25\) lego pieces in a box:
In how many ways are there to choose three pieces to play with?
In how many ways can he choose three pieces for the foundation, main walls and roof? Note that the order is important.
Doctor Smith gave out 2006 miracle tablets to four sick animals. The rhinoceros received one more tablet than the crocodile. The hippopotamus got one more tablet than the rhino. The elephant got one more tablet than the hippo. How many tablets did the elephant have to eat?
Gabby is standing on a river bank. She has two clay jars: one – for 5 litres, and about the second Gabby remembers only that it holds either 3 or 4 litres. Help Gabby determine the capacity of the second jar. (Looking into the jar, you cannot figure out how much water is in it.)
There are two numbers \(x\) and \(y\) being added together. The number \(x\) is less than the sum \(x+y\) by 2000. The sum \(x+y\) is bigger than \(y\) by 6. What are the values of \(x\) and \(y\)?
On Brennan’s birthday, the postman Daniel wants to find out how old Brennan is. Sarah says that Brennan is over 11 years old, and Matt claims that he is more than 10 years old. How old is Brennan, if it is known that exactly one of them was mistaken? Justify your answer.