Number Play — Class 8 Mathematics

Number Play uses algebra, visualisation and reasoning to explore parity, divisibility and number puzzles. Beginning with sums of consecutive numbers and the parities of expressions , it shows all such combinations share the same parity. Algebra explains when expressions are always even — for example is always even. The chapter develops general divisibility rules and proves why they work: divisibility by from the units digit; by and from the digit sum (since each place value is one more than a multiple of ); and by from the alternating digit sum (since place values alternate one more and one less than a multiple of ). Key divisibility laws are established: if divides and , it divides and ; if is divisible by then so are all multiples of ; and if a number is divisible by both and , it is divisible by their LCM. Digital roots and cryptarithms — puzzles where letters stand for digits — round out the playful but rigorous tour.