Multiplication and division

Two numbers can be placed adjacent if one of them divides the other. Using only $1,...,10$, can you write the longest such list?

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Choose any four consecutive even numbers. Multiply the two middle numbers together. Multiply the first and last numbers. Now subtract your second answer from the first. Try it with your own numbers. Why is the answer always 8?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

How much lighter will £5 worth of 5p's be with these new lighter coins?

What could be the scores from five throws of this dice?

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?