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?

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

The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

What is the remainder when 2^{164}is divided by 7?

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?