Multiplication and division

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?

Can you produce convincing arguments that a selection of statements about numbers are true?

Vedic Sutra is one of many ancient Indian sutras which involves a cross subtraction method. Can you give a good explanation of WHY it works?