Help! I'm stuck!

Here are some general hints that may help you if you get stuck.

Stop and think.

If you get stuck, the first thing to do is stop for a minute and think about what you are trying to do. This is a good thing to do if you are making your very first move--or if you are in the middle of moving a stack. It's easy to lose track of where you are in this puzzle--and it helps to stop and think.

Think about your goal. Then think about what's stopping you from getting to that goal.

Look ahead.

Sometimes, you want to move a coin--because it's on top of the coin that you really want to move. When you do that, be careful that you don't put the coin you're moving in the spot that you want to put the next coin. Try to look one move ahead.

Go back to an easier problem.

If you get stumped when you are trying to move a stack of 4 coins, go back and try moving a stack of 3 coins again.

Why bother to do that? Well, in order to move a stack of 4 coins, first you need to move the stack of 3 coins off the bottom coin. So remembering how you moved a stack of 3 coins will help you move 4.

Also, you use the same basic moves whenever you move a stack. So moving a stack of 3 is great practice for moving a stack of 4.

Look for patterns.

As you move coins, look to see if you can see any patterns in the way that you move them. For instance, suppose you are moving the stack of 3 coins. You start by moving the dime to the right circle. Where does the stack end up when you are done? Does the stack end up somewhere else if you start by moving the dime to the left circle?

Keep track of your moves

When you're moving a stack of 5 or 6 coins, it can be handy to know what you've already moved--so that if you get stuck, you can figure out where you went wrong.

What if I'm still stuck?

Look at the answer below.

What's the Answer?

Don't give up too soon. For the first puzzle, "Beginning Mindbender," we talk you through the answer, telling you stuff that you might want to think about along the way. For the other puzzles, we tell you the answers in short hand notation.

Beginning Mindbender: Moving 3 coins in 7 moves

The first move is easy--you move the dime off the top of the stack into one of the other circles. The second move is easy, too--you can't put the penny on top of the dime, so you have to move it to the other empty circle. Now you have one coin in each circle.

You want all the coins to end up in the left or the right circle--not the middle circle, since that's where they started. To manage that, you have to empty the left or right circle. How can you do that? Well, you can put the dime on top of the penny. That empties one circle. So you move the nickel to the empty circle and you're almost there. You can't move the penny because the dime is on top of it. So you move the dime to the empty middle circle. Then you move the penny to the left circle, on top of the nickel. And you're home free--you can put the dime on top of the penny, and the stack is moved!

Using shorthand notation, here's how to move the stack of 3 coins in 7 moves and make sure they end up in the right circle:

Thank you for testing this activity. We would appreciate your comments and suggestions. Please send us an email with your ideas. Thanks for helping out!

©1997 The Exploratorium