HELEN DIVIDES 365 BY EACH OF 1, 2, 3, . . . , 365 IN TURN, WRITING...

1. Helen divides 365 by each of 1, 2, 3, . . . , 365 in turn, writing down a list

Time allowed 3

hours.

of the 365 remainders. Then Phil divides 366 by each of 1, 2, 3, . . . , 366

Instructions • Full written solutions – not just answers – are

in turn, writing down a list of the 366 remainders. Whose list of

required, with complete proofs of any assertions

remainders has the greater sum and by how much?

you may make. Marks awarded will depend on the

clarity of your mathematical presentation. Work