Problems

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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 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?

The intelligence agency of the Galactic Empire intercepted the following coded message from the enemy planet Medusa: \(ABCDE+BADC=ACDED\).

It is known that different numbers are represented by different letters, and that the same numbers are represented by the same letters. Two robots attempted to decode this message and each one got a different answer. Is this possible, or should one of the robots be melted down as scrap metal?

In a room there are some chairs with 4 legs and some stools with 3 legs. When each chair and stool has one person sitting on it, then in the room there are a total of 39 legs. How many chairs and stools are there in the room?

Carpenters were sawing some logs. They made 10 cuts and this produced 16 pieces of wood. How many logs did they saw?

Snow White cut out a big square of cotton fabric and placed it in a chest. The first gnome came, took out the square of fabric from the chest, cut it into four squares, put these back in the chest and left. Later the second gnome came and took out one of the squares and then cut it into four pieces and placed all of these in the chest. Then came the third gnome. He also took out one of the squares and cut it into four squares and put them all back in the chest. The rest of the gnomes also did the same thing. How many squares of fabric were in the chest after the seventh gnome left?

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 \(y\)?