## Sunday, April 30, 2006

### NCTM Fun

I had a great time with my coworkers in St. Louis at the NCTM conference. I went to talks on assessment, questioning, struggling learners, fun math, challenging brain stretchers .... I'm revitalized to end our school year.

Here's one puzzle I got from a presenter. She puts up a new line every day, and her students have to guess the pattern (and/or guess the next row of numbers). I'll put up a few, but of course it goes up in stages and can go on forever (and lead to interesting follow up questions).

1
11
21
1211
111221
312211
....

1. Anonymous7:17 PM

Alright, I'm frustrated enough to ask....what exactly is the pattern? At first I was looking for a Pascal's triangle type of connection, but I didn't get it....

2. Anonymous8:49 PM

I'll give you the next 2 lines (mwa ha ha ha)

13112221
1113213211
...

and a hint: every line is related to the line before it. I'm glad you're trying it.

3. Anonymous5:01 AM

2 more lines and another clue ...
31131211131221
13211311123113112211

clue: description

4. Anonymous10:22 PM

I was the orginal asker here....I figured it out. I actually had guessed it but then I thought that it didn't work because I made a mistake. I think I'll use this at the end of the year as an extra credit question. :) Thanks.

5. Anonymous4:58 AM

Great! I love when I finally figure out a challenging puzzle.

Here's a follow up question: will there ever be any "4"s in the sequence? "5"s .... How can you prove it?

6. Anonymous5:33 AM

I'm pretty sure the answer to the 4's question is no....when you get big enough to be described by a three you prevent another one being added in the next line....you'll never say there's one one and then right next to it say there's one one again (making 4). What other way(s) can you prove it?

7. Anonymous5:43 AM

I was thinking along the same lines and going for a proof by contradiction. Suppose you have "...41..." in your sequence. That means in the previous row you had 4 ones. Which means that was describing 2 rows back with "one 1 and one 1" which is not how it would be described (contradiction).

8. Anonymous2:46 PM

This is my favourite all time puzzle. :)

I didn't know how to prove you couldn't ever have a four in it, although I worked out that you couldn't. I just wasn't sure how to put it into words.

Owl.

9. Anonymous4:36 PM

I know. How cool is it? I guess it's that it's easy to remember the set up. It's straightforward, and it's challenging.