11 scouts are working on 5 different badges. Prove that there will be two scouts \(A\) and \(B\), such that every badge that \(A\) is working towards is also being worked towards by \(B\).
Is it possible to place the numbers \(-1, 0, 1\) in a \(6\times 6\) square such that the sums of each row, column, and diagonal are unique?
There are bacteria in a glass. After a second each bacterium divides in half to create two new bacteria. Then after another second these bacteria divide in half, and so on. After a minute the glass is full. After how much time will the glass be half full?
Anna, Vincent, Tom and Sarah each bought one apple for 10p from a fruit stand. How did they manage to do this, if they didn’t have any coins less than 20p and if the fruit stand didn’t have any change less than 50p?
A piece fell out of a book, the first page of which is the number 439, and the number of the last page is written with those same numbers in some other order. How many pages are in the fallen out piece?
A snail crawls along a wall, having started from the bottom of the wall. Each day the snail crawls upwards by 5 cm and each night it slides down the wall by 4 cm. When does it reach the top of the wall, if the height of the wall is 75 cm?
In January of a certain year there were four Fridays and four Mondays. Which day of the week was the 20th of January in that year?
A rectangle of size \(199\times991\) is drawn on squared paper. How many squares intersect the diagonal of the rectangle?
Imogen’s cat always sneezes before it rains. Today the cat sneezed. “So, it will rain” thinks Imogen. Is she right?
Three tortoises crawl along the road in a line. “Two tortoises are crawling behind me,” says the first. “One tortoise is crawling behind me, and one tortoise is crawling in front of me,” says the second. “Two tortoises are crawling in front of me, and one tortoise is crawling behind me,” says the third. How can this be?