In: Advanced Math
(a) Can the sum of 12345 odd pos-
itive integers be 12345678 ? Prove or disprove.
(b) Prove that for every possible re-arrangement (b1, b2, . . . ,
b999) of the
numbers (1, 2, . . . , 999), the product
(b1 − 1)(b2 − 2)(b3 − 3) · . . . · (b999 − 999) is even.