20-CS-110-001 |
Introduction to Computer Science |
Fall 2010 |
---|

**Solution to Powers Puzzle**

Looking at the consecutive powers of seven, starting with one, we see
that the unit's place of 7^{1} = 7, 7^{2}= 49,
7^{3}= 343, 7^{4} = 2401, and 7^{5}=16807.
Looking at just the unit's place, we have the repeating series
7,9,3,1,7,9,3,1..., which repeats every 4 numbers. Since 1000 is
divisble by 4 (the cycle length), the 1000th term of this series is
the same as the fourth term, which is 1. |