I recently got an email from the creator of a puzzle called Hexa-Trex.  As the name suggests the puzzle involves hexagons.  The hexagons are laid out in a pattern chosen by the puzzle designer and each has either a digit or an arithmetic operator inside.  The goal is to find a path through all of the hexagons exactly once to create a valid mathematical equation.  New puzzles are posted every couple of days and the range from very easy to quite challenging.  Enjoy.

There’s an interesting article on Science News Online about puzzles and the mathematics behind solving them.  The article looks specifically at two puzzles that are available from ThinkFun.

The first is TipOver, also sometimes known as crate puzzles.   There’s a Java implemention that’s ready to play at PuzzleBeast.  In the puzzle, there are stacks of crates of varying heights positioned around the room.  You begin the puzzle on one stack of crates and the goal is to move to a crate that is marked as the goal.  You may move from crate to crate, but you can’t touch the floor or jump over empty space.  You may also knock over a stack of crates if there’s room.  The article gets pretty serious into the math.  Turns out the problem in NP-complete.  You should check out the article if you want to know more.

The second puzzle is River Crossing, also sometimes known as plank puzzles.  These puzzles were designed by Andrea Gilbert at clickmazes.  In this puzzle, your goal is to cross a river gong from tree stump to tree stump using a limitted set of planks of varying length (again no jumping or swimming through the river.)  This puzzle is PSPACE-complete.

Without getting too far into it here, the most interesting thing about NP-complete and PSPACE-complete problems is that there’s no known efficient algorithm for solving them.   If you can one, you may win $1 million.

It’s a simple puzzle with fancier stuff promised in the future.

The puzzle asks you to take the numbers 3, 3, 8, and 8, arrange them in a specific order and create a mathematical expression that equals 24. You can use addition, subtraction, multiplication, and division. All of the numbers must be used.

Here’s a word equation puzzle from mathpuzzle.com:

A+L+P+H+A=1, B+R+A+V+O=2, C+H+A+R+L+I+E=3, D+E+L+T+A=4, E+C+H+O=5, F+O+X+T+R+O+T=6, G+O+L+F=7, H+O+T+E+L=8, I+N+D+I+A=9, J+U+L+I+E+T=10, K+I+L+O=11, L+I+M+A=12, M+I+K+E=13, N+O+V+E+M+B+E+R=14, O+S+C+A+R=15, P+A+P+A=16, Q+U+E+B+E+C=17, R+O+M+E+O=18, S+I+E+R+R+A=19, T+A+N+G+O=20, U+N+I+F+O+R+M=21, V+I+C+T+O+R=22, W+H+I+S+K+E+Y=23, X+R+A+Y=24, Y+A+N+K+E+E=25, Z+U+L+U=26

The goal of the puzzle is to solve for each individual letter. There’s also an interesting discussion on the site about how to find a complete set of words that result in a single, unique solution. This is the kind of puzzle where I appreciate the form even if I don’t think I would particularly enjoy solving it.

I was introduced today to a puzzle called “Petals Around the Rose” on the nan (not a nerd) blog. This is the kind of puzzle that might be called a “definition puzzle.” The solution to the puzzle is trivially easy, the trick lies in defining the problem.

The puzzle set up goes as follows. Roll five six-sided dice. Then answer: How many petals around the rose? There is only one answer. The answer is always even and, sometimes, it’s zero. To try it out, there’s a flash based simulation on this page. I’ll give the author of the page the benefit of the doubt and assume it works in some browsers, even though it didn’t work in mine. Another implementation of the puzzle can be found here.

They say that some solve the puzzle quickly and others require a long time. Having solved the puzzle, I can say that it’s not the most diabolical of its kind.