Wednesday, September 17, 2008

my all time favorite problem


Fill in the following sentence to make the sentence true:

There is ___ 0's, ___ 1's, ___ 2's, ___ 3's, ___ 4's, ___ 5's, ___ 6's, ___ 7's, ___ 8's, and ___ 9's in this sentence.

Note: First, there are two solutions. Second, this is one of my favorite all time problems. I found it in a Doug Hofstadter book, Metamagical Themas. Aparently Abraham Robinson, inventor of non-standard analysis, came up with the problem. I've had students look this up online for the answer. One even found a site that treated this as the base 10 version of a larger set of problems. He was able to generalize a solution. Very cool! Make sure to try it first though.

4 comments:

HM said...

Sue was being a wise-%$&, and wanted to fill in each blank with the word 'one'. No good!

She was also trying to say that if she put 10 into one of the blanks. It wouldn't count as both a 1 and a 0. This is also cheating the problem. What is interesting about this question is that the question's meaning concerns its own representation. So a ten in any blank contributes to the number of 1's and 0's in the representation.

Sue said...

OK--so I had to do it right. Here's the solution

1 0's 7 1's 3 2's 2 3's 1 4's 1 5's 1 6's 2 7's 1 8's and 1 9's

Perhaps not grammatically correct--that is how the problem is written--but it works. Maybe someday I'll be geek of the week.....

Anonymous said...

I would like to point out that I was the original wise-@$$ who filled in all the blanks with the word "one" in your Liberal Arts class last semester.

And I still believe it to be a perfectly acceptable third solution to this problem.

-jeff m

HM said...

I'm of the mindset the wise-#@$-ery just cheapens the problem. But you're right, you were the original. How could if forget! I'm still recovering.