Multiplication and division

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

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

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

Find the highest power of 11 that will divide into 1000! exactly.

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by 3, 5 and by 7...

6! = 6 × 5 × 4 × 3 × 2 × 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4) = 45. What is the highest power of two that divides exactly into 100!?

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain why this works.

Can you reconstruct the long division calculation from the 'skeleton'?

This Sudoku requires you to do some working backwards before working forwards.