As an odometer check, a special counter measures the miles a car travels modulo 7. Explain how this counter can be used to determine whether the car has been driven 49335; 149335; or 249335 miles when the odometer reads 49335 and works modulo 100000.

Question

tkhunny · Answer

100000 = 5 mod 7

149335 mod 7 = 49335 mod 7 + 100000 mod 7 = [(49335 mod 7) + 5] mod 7

249335 mod 7 = 49335 mod 7 + 10 mod 7 = [(49335 mod 7) + 3] mod 7