Marys watch keeps perfect time and bills watch loses 4 minutes a day.
both watches are set at midnight on january 1. how many times a year will they match?

Three times a year because every 144 days Bill’s watch will loop. This is proven by the fact that of course 60*24 equals 1,440 and if we divide by 10 (because it’s ten minutes and not one) we get 144 and 144*2 equals 288 but 144*3 equals 432 which would go over one year so it will loop two times plus the start of the year making three