Problem:
Every positive integer k has a unique factorial base expansion (f1,f2,f3,…,fm), meaning that k=1!⋅f1+2!⋅f2+3!⋅f3+⋯+m!⋅fm, where each fi is an integer, 0≤fi≤i, and 0<fm. Given that (f1,f2,f3,…,fj) is the factorial base expansion of 16!−32!+48!−64!+⋯+1968!−1984!+2000!, find the value of f1−f2+f3−f4+⋯+(−1)j+1fj.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions