## Sunday, January 7, 2007

### 2007. 7 and 35

Problem 7
Difficulty: so easy the kids kept second-guessing themselves. ;-)

Problem 35
Difficulty: Hard (last page)

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 7 and answer 35.

#### 3 comments:

1. I like this one. Even had I not encountered this problem before, I would have suspected the structure of the factors was key. Solve for 3, 9, 27, 81... see if I can pull out a pattern. The danger is trying powers of 2, which work quite differently.

(I think I have mentioned - I teach a variation of this)

Jonathan

2. I like this one. Even had I not encountered this problem before, I would have suspected the structure of the factors was key. Solve for 3, 9, 27, 81... see if I can pull out a pattern. The danger is trying powers of 2, which work quite differently.

(I think I have mentioned - I teach a variation of this)

Jonathan

3. That's odd, Jon. What's your argument?
I worked with powers of five and two conditions, one where the middle term was x and p was odd and then one where the lower of the two middle terms was x and p was even. I got an answer and confirmed it so now I'm completely mindset and can't for the life of me figure out where powers of 3 are going in this.
Help!