When Gulliver came to Lilliput, he found that there all things were exactly 12 times shorter than in his homeland. Can you say how many Lilliputian matchboxes fit into one of Gulliver’s matchboxes?
Three hedgehogs divided three pieces of cheese of mass of 5g, 8g and 11g. The fox began to help them. It can cut off and eat 1 gram of cheese from any two pieces at the same time. Can the fox leave the hedgehogs equal pieces of cheese?
Gerard says: the day before yesterday I was 10 years old, and next year I will turn 13. Can this be?
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?
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 \(y\)?
Henry did not manage to get into the elevator on the first floor of the building and decided to go up the stairs. It takes 2 minutes to rise to the third floor. How long does it take to rise to the ninth floor?
In a class there are 50 children. Some of the children know all the letters except “h” and they miss this letter out when writing. The rest know all the letters except “c” which they also miss out. One day the teacher asked 10 of the pupils to write the word “cat”, 18 other pupils to write “hat” and the rest to write the word “chat”. The words “cat” and “hat” each ended up being written 15 times. How many of the pupils wrote their word correctly?
We call a number \(x\) rational if it can be represented as \(x=\frac{p}{q}\) for coprime integers \(p\) and \(q\). Otherwise we call the number irrational.
Non-zero numbers \(a\) and \(b\) satisfy the equality \(a^2b^2 (a^2b^2 + 4) = 2(a^6 + b^6)\). Prove that at least one of them is irrational.
The real numbers \(x\) and \(y\) are such that for any distinct prime odd \(p\) and \(q\) the number \(x^p + y^q\) is rational. Prove that \(x\) and \(y\) are rational numbers.
Looking back at her diary, Natasha noticed that in the date 17/02/2008 the sum of the first four numbers are equal to the sum of the last four. When will this coincidence happen for the last time in 2008?