Tag: puzzles

The Tower of Hanoi Math Game
One of my favorite math games as a kid was The Tower of Hanoi. I had no idea what it was called until college, though. To me it was another cheap wooden puzzle. Or a game you could play with four coins and 10 toothpicks.

The object of the game:
- Move the stack from where it is, to another square or post.
The rules of the game:
- You can only move one disk (or coin) at a time.
- You can only put a disk (or coin) on top of one that’s bigger – physically. (I.e. you can’t put a big one on top of a smaller one.)
You can play it online for free or buy a physical version in classic or kid-friendly versions.

How can you use The Tower of Hanoi with your kids?

In the Tower of Hanoi puzzle, the math is vast – especially for such a simple little puzzle. But the math can be discovered gradually.

Present these challenges to your kids, one at a time:
1. Move the stack according to the rules (just get it to another place.)
2. Move the stack according to the rules in as few moves as possible. How many moves is that?
3. Make the stack smaller or larger. Then move the stack according to the rules in as few moves as possible. How many moves is that?
4. Repeat challenge #3 with many different numbers of coins/disks. Use cut out pieces of paper if necessary.
5. Determine how many moves it would take to move a stack of 100 disks. Or 1000 disks.
6. Then figure out a way to say this without numbers. In other words, create some sort of formula that will tell you how many moves you need to move any number of disks.
These challenges might range over many many years. I first learned of The Tower of Hanoi when I was about ten. And I’m still learning about it 30 years later.

Oh, and try to resist giving them any answers – ever. Instead let them work on it in their spare time.

Your turn!

Have you played The Tower of Hanoi math game, or a version of it? Do you remember the first time you came across it? Did you learn or teach math with it?

And how will you introduce it to your kids?

Share your thoughts in the comments!

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February 27, 2012
Frabjous Puzzle Sculpture from the Museum of Mathematics
MOMath, the Museum of Mathematics, sent me their new puzzle Frabjous – a design by George W. Hart.

I had to wait for Daughter to be in bed before digging in – the box states, “Recommended for ages 16+.”

I was pretty sure that a precocious 10 year old could handle it but I was unwilling to risk a 2 year old eating my cool puzzle.

My “solution” to the puzzle…

Oh, my… all the pieces are exactly the same!

No biggie, though – I’m pretty smart. “I can do this!” I thought.

I thought.

After a while, I felt like maybe I was doing it right, and maybe not. Here’s the view from the top when I had 12 of the 30 pieces left to go:

Guess what – the instructions clearly state “check that no parts are touching in the interior.”

Everything in mine is touching!

I’m (maybe) throwing in the towel!

I keep looking at the mostly-built thing. It’s pretty, even in its unfinished state. I’m not one to quit, but I will pause temporarily.

So for now, I have the wad of blue looking at me everyday. Staring. Saying, “Are you smart enough to finish me?”

Sometimes I tell it to hush.

Sometimes I google it.

Windell Oskay, an Evil Mad Scientist, has some great images on his writeup of making your own Frabjous. I’ll likely use these when I get the courage tackle this thing again.

I could just watch the video.

I’m against looking in back-of-the-book answer pages. So I’m certainly not about to let a video tell me how to work a puzzle.

But my cantankerous attitude doesn’t mean that you get deprived. Here’s the video:

You can buy the Frabjous online for $29 plus about $7 shipping within the U.S. Technically, you can save the $36 bucks and build your own. But that might be a real pain. Plus, if you buy it from the Museum of Mathematics, you support them!

What do you think? Do you want one? Have you built one? Share your thoughts and links to pictures in the comments.

The Museum of Mathematics (MOMath) will open in New York City in 2012.

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February 1, 2012
HELP – Logic Puzzle Announcing The Homeschool Blog Awards
Okay, y’all, I’m in over my head. I’m trying to create a logic puzzle as a nifty way to announce The Homeschool Blog Awards. Having never created a logic puzzle before, I thought, “How hard can it be?”

Well, pretty darn hard.

So I thought I’d put my start out there, as well as the solution, and see if I can get some help from y’all.

Read the puzzle, try to figure out the solution, then suggest in the comments one or more clues that I should add (or get rid of).

The Puzzle

The Homeschool Post is the sponsor of The Homeschool Blog Awards every year. Writers of The Homeschool Post aren’t allowed to win, nor be nominated. So some of the writers of thought it might be fun to do a “within the family” blog award for themselves.

After all was said and done, they decided to pass all information over to me, the math mom in the team, and let me figure out the winner. Alas, the information wasn’t well organized. So I had to figure out which blog went with which person, who voted for whom and who was the winner.

The Clues

Six of the writers decided to participate. They were
- Lana (like Banana)
- The writer of OK Homeschool Mom
- Heather
- The writer of Knit 1 Kids 4
- Gidget
- Rachel
1. Heather said, “I love everyone. I’m just voting for them all!”
2. Someone suggested that nobody should vote for themselves. So they agreed on that.
3. The writer of Finding Joy voted for three people, including Heather and Kristal.
4. Everyone who voted for Rachel also voted for the blog I Love My 5 Kids.
5. Everyone but Gidget voted for the author of the blog SprittiBee.
6. The author of Homeschooling Unscripted only got two votes.
7. Donnetta and Gidget got the same number of votes. As did the authors of SprittiBee and Knit 1 Kids 4. Also, Rachel and the author of I Love My 5 Kids had the same number.
8. The author of Finding Joy is very popular – everyone voted for her.
The Solution

Here is the solution of who voted for whom. The initial of the person is on the left and the initial of the people for whom they voted is in the curly brackets. Click on the picture to enlarge.

Owners/writers of the blogs are here:
- Donetta publishes OK Homeschool Mom
- Gidget publishes Homeschooling Unscripted
- Heather publishes SprittiBee
- Kristal publishes Knit 1 Kids 4
- Lana publishes I Love My 5 Kids
- Rachel publishes Finding Joy
Don’t forget…

Suggest a clue in the comments!

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October 13, 2011
In How Many Ways Can You Solve the Thiagi Circles Jolt?
I was at a seminar yesterday with world famous (and awful fun) Thiagi. He keeps his participants on their toes with small activities called jolts. Jolts are defined at interactive experiential activities and:

…force participants to re-examine their assumptions and revise their habitual practices.

One jolt we did yesterday got me to thinking about math. Okay, many of them had me thinking about math. But this one was about the multiplication principal of counting and sets.

The multiplication principal says that if you have 7 ways to do the first thing and 3 ways to do the 2nd thing, then you’ll have 3 * 7 = 21 ways to do them together. Assuming you pick one of each.

So if I want a sandwich (tuna, ham or turkey) and a side (chips, onion rings, fruit or fries) for lunch, I will have the option of 3 * 4 = 12 different lunches.

The Thiagi Circles Jolt

Here is the Circles Jolt that Thiagi offered: Draw this figure without ever lifting your pencil or retracing over any lines (or curves):

It isn’t hard, as you probably see. It takes anywhere from 10 to 45 seconds to figure it out. The question is, “Is there another way to do it than the one I thought of?”

So here are the ways I immediately thought of in the Thiagi Workshop:

The fancy pants teacher’s pet, Mark, was asked to demonstrate the answer. And he did it in an even different way! So I saw that there were 8 more ways to do it:

Trying to trump Mark and be the new teacher’s pet, I announced that there were indeed 16 ways to accomplish Thiagi’s goal.

And here I am. Still trying to win the favor of the teacher by producing the 16 ways via blog and video.

There are 16 ways because of the Multiplication Principal of Counting.

Notice there are four questions to answer when solving this:
1. Do you start from left or right side of the drawing?
2. Do you start by drawing the outer circle or go through and start at the inner circle?
3. Do you go up or down on the first circle you draw?
4. Do you go up or down on the second circle?
Each question has two different options. So there are

2 sides to start from * 2 circles * 2 directions to go in the 1st circle * 2 direction in the 2nd circle

2 * 2 * 2 * 2 = 16 different ways to draw the diagram!

Teach this with experiments.

Although you now know how many there are, don’t teach it this way. Instead, just give the jolt to the kids. Once they solve it, show them “your way,” which should be any way that is different than theirs.

Then tell them that for ever unique solution, you’ll give them $1. (Thiagi gave out $1 bills yesterday, too!)

Once they come up with all 16, offer the extra $4 for some way they can show the number 16 with numbers (logically based on their solutions). They might come up with 2 * 8 or 4 * 4, as long as they can group their drawings in logical bundles.

What do you think?
April 28, 2011