Place value

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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" .

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

What is the smallest perfect square that ends with the four digits 9009?

Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers and so on?

If the last four digits of my phone number are placed in front of the remaining three you get one more than twice my number! What is it?

Suppose you had to begin the never ending task of writing out the natural numbers: 1, 2, 3, 4, 5.... and so on. What would be the 1000th digit you would write down.

Find b where 3723(base 10) = 123(base b).