Place value

The number 3723(in base 10) is written as 123 in another base. What is that base?

What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?

Find the five distinct digits N, R, I, C and H in the following nomogram

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

Weekly Problem 48 - 2013
What is the remainder when the number 743589×301647 is divided by 5?

This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.

115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?

In this addition each letter stands for a different digit, with S standing for 3. What is the value of YxO?

A school song book contains 700 songs. The numbers of the songs are displayed by combining special small single-digit cards. What is the minimum number of small cards that is needed?