Saturday, November 10, 2012

Like Brainteasers?

So do middle school kids.

Sometimes, when we finish a couple of minutes early, I like to do a couple with the class.

I've been using the same ones for several years, and it's interesting to see how quickly (if at all) the kids can figure them out. A few of my favorites follow. Now, I know that the Google search bar is just a few inches up, but no cheating!

(Don't worry - answers included below)! 
Feel free to post your favorites!

Truth-Tellers and Lie-Tellers
You're walking through the woods, and you come to a fork in the path. You know that one direction leads to the Truth-Teller Village (where everyone always tells the truth), and the other leads to the Lie-Teller Village (where everyone always lies). At the fork in the road is an old man. You don't know whether he is a Truth-Teller or a Lie-Teller, but you are allowed to ask him one question. Your goal is to reach the Truth-Teller Village.
What question do you ask? 


The Pattern

Take a look at the pattern to the left.
What comes next?

I love the "Ooooohhhhhhhhh," I get from kids on this one.


Given the arrangement of pennies to the right,
move exactly one penny and create one row
and one column each containing exactly four pennies.


And, the mother of them all...

1 11 21 1211
Given the following pattern, what is the next line?


After a couple of minutes, I usually tell the kids that...
1. The math involved isn't anything a kindergartner couldn't do.
2. I never figured it out. Someone had to tell me (although I tried it for two weeks).
3. Just for fun, I usually tell them the next line - 111221 - and ask for the one after that.
    (It goes on forever) 


Brainteaser Answers

Truth-Tellers and Lie-Tellers
You ask, "Which way to your village?"
A Truth-Teller tells the truth and points toward the Truth-Teller village.
A Lie-Teller tells a lie and points toward the Truth-Teller village.   

The Pattern

Given the image
to the left, I think
we can declare
this one solved!


Place the uppermost
penny directly on top
of the center penny.

Four across, four down!   

1 11 21 1211
This is a "say what you see pattern.
Each line, when read out loud, describes the line immediately above it:

                            11             "One 1"
                            21             "Two 1's"
                        1211          "One 2, One 1"
                      111221       "One 1, One 2, Two 1's" 

So, the next line would be...312211
That's, "Three 1's, Two 2's, One 1" 

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