No Integer Solutions

About numbers in a circle. and how to possibly make them equal.
How can you find the sides of a rectangle that has the same area as a given square without a compass, without a ruler – even without a pencil – if all you have available is a postcard?
Draw 4 straight lines in a cross figure to represent a single square of equal area.
How many 10-digit numbers with different digits are there?
What is the largest three-digit (whole) number of a particular type?
Can you represent the number one billion as the product of two integers m and n such that neither m nor n ends in the digit 0?