Place value

Can you verify and generalise these equations?

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

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.

There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. Can you work out in which direction the Zios and Zepts were looking, based on the information you're given?

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

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

Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

What is the sum of all the digits in all the integers from one to one million?

Can you explain what's happening with these numbers?