Taxes In a warehouse you obtain 20% discount but you must pay a 15% sales tax. Which would you prefer to have calculated first: discount or tax?

Tethered Goat A goat is tethered by a 6 metre rope to the outside corner of a shed measuring 4 metres by 5 metres in a grassy field. What area of grass can the goat graze?

Children Ages Two friends are chatting: John: How old are your children now? Eric: Well, there are 3 of them, and if you multiply their ages together you get 36. John: Can you give me more information? Eric: OK, the sum of their ages is exactly the number of biscuits we just consumed. John: That’s still not enough. Eric: OK, my oldest child likes to do maths puzzles. John: OK, now I have worked it out. How old were each of Eric’s children?

The Locker Problem 1,000 students march slowly through their school, going past 1,000 lockers. The first student opens every locker along the way. Then the second student comes along and shuts every second locker. Then the third student reverses the condition of every third locker, and then the fourth student reverses the condition of every fourth locker. The students continue in this manner (e.g., the 99th student reverses the condition of every 99th locker, etc.). After all students have gone through the school, which lockers remain open?

Palindromes A number like 12321 is called a palindrome because it reads the same backwards as forwards. A friend of mine claims that all palindromes with four digits are exactly divisible by 11. Are they?

Ladies at a Table Five women have lunch together seated around a circular table. Ms Osborne is sitting between Ms Lewis and Ms Martin. Ellen is sitting between Cathy and Ms Norris. Ms Lewis is between Ellen and Alice. Cathy and Doris are sisters. Betty is seated with Ms Parkes on her left and Ms Martin on her right. Match the first names with the surnames.

What is the Product? What is the following product? Why? (𝑥−𝑎)(𝑥−𝑏)(𝑥−𝑐)(𝑥−𝑑) . . . (𝑥−𝑦)(𝑥−𝑧) Hint: Don’t spend ages trying to multiply this out: it’s meant to be funny (insofar as maths can by funny).

Toast Three slices of bread are to be toasted under a grill. The grill can hold two slices at once but only one side is toasted at a time. It takes 30 seconds to toast one side of a piece of bread, 5 seconds to put a piece in or take a piece out and 3 seconds to turn a piece over. What is the shortest time in which the three slices can be toasted?

Painted Tyres Once while riding on my bicycle along a path I crossed a strip of wet paint about 6 inches wide. After riding a short time in a straight line I looked back at the marks on the pavement left by the wet paint picked up on my tyres. What did I see?