Puzzle Corner

2010-06-12
When 2^301 is divided by 5, the least positive remainder is ......
1. 4
2. 8
3. 2
4. 6

2010-06-10
The equation X-[2/(X-1)] = 1-[2/(X-1)] has
1. no roots
2. one root
3. two equal roots
4. infinite roots

2010-06-09
If (1+3+5+...+p)+(1+3+5+...+q) = (1+3+5+...+r), where each set of parentheses contains the sum of consecutive odd integers as shown, what is the smallest possible value of (p+q+r), where p>6?
(a) 12
(b) 21
(c) 45
(d) 54