## Morris: Turning Tables

I took one of Peter Winkler’s puzzle books on holiday recently. After dinner each night I intended to impress my friend with an amazing math puzzle. I had done this before.

The book dissapeared on the flight out. After dinner each night my friend impressed me with an amazing math puzzle. I haven’t seen the book since.

Serves me right!

This is one of those puzzles, you will understand why I have to do it from memory.

I really like Jeff’s post A Fun Trick – Guess the Polynomial. You might want to look at it first.

If you relax the conditions a bit you have a similar sounding puzzle with a very different solution.

So my puzzle is this:

I am thinking of a polynomial. All of the co-efficients are fractions. You may use any number as your test number. When you give me a test number I will tell you the result.

How many test numbers do you need to identify the polynomial?

## czarandy said,

April 20, 2009 at 7:51 pm

[spoiler]

It seems like you need n+2, if n is the degree of the polynomial.

[/spoiler]

## Stephen Morris said,

April 21, 2009 at 1:41 pm

Thanks czarandy. I’ve spent a couple of hours thinking about your answer. It was fun so thanks! Also it is good material for a follow up post.

I’ve just edited this because I’ve realised I’ve missed a case: [spoiler]what if the test numbers can only be algebraic numbers (E.g. 3, 47/236, sqrt(59) but not pi or e)? My proof by contradiction doesn’t work. Is the answer n+2? I need more time to think about it! Would love to see your working![/spoiler]