40 30s 4 15

Published on Thursday, June 30, 2005 in , , , ,

What I'm about to describe isn't so much a performance piece. Instead, it's more of a tool to create an offbeat surprising moment when the opportunity presents itself.

This unusual feat concerns the classic 15 puzzle, created by Sam Lloyd. Next time someone hands you either a real or virtual version of the 15 puzzle with the numbers 1 through 15 on it, you'll be able to hand it back to them with a magic square on it!

In order to be able to do this, you'll need to work through the following process, step by step:

1) Obviously, the first step is to learn how to solve the fifteen puzzle in the standard manner. Practice this step until you're comfortable, and can solve the puzzle with confidence.

2) Next, you're going to learn to solve the puzzle in a manner such that the pieces form a magic square. Here is the arrangement in which you need to put the tiles:

14 3 8 5
9 4 15 2
7 10 1 12
13 6 11

Note that the empty space in this arrangement is in the bottom left, instead of the bottom right as in the standard pattern. To adjust for this difference, you'll be using the same technique as in step 1, but you need to solve the bottom two rows from right to left.

This arrangement is a perfect magic square, and will total 30 in all of the 40 different ways described in section 3.2.5 of this magic square article, which is why the article is titled "40 30s 4 15" (Translation: "Forty '30s' for the 15 puzzle").

3) Once you feel comfortable solving the 15 puzzle for this new pattern by looking at the diagram, the final step is to memorize the number arrangement. To do this, you'll need to be familiar with the Major System.

Instead of simply memorizing the arrangement from left to right and top to bottom, the arrangement will be memorized in an order that works with the solution process.

Here's the story that you need to memorize, with the key words in bold:

I had a dream that I could fly. During this, I came across a pretty lion.

Now, his dad had a tan. He got onto a jet, which was filled with lots of tomatoes and one single sock.

Each of the bold words above represents a word that must be remembered, and is translated into a series of numbers.

The words in the first sentence, dream and fly, break down into 14-3-8-5, which is how you need to arrange the top row.

The second sentence describes the arrangement in the second row, with pretty and lion breaking down into 9-4-15-2.

From here on out, the phrases work from the bottom up, and from right to left, because that is how the tiles will be placed.

Dad and tan translate, respectively, to 11 and 12. This is to remind you to place 11 in the bottom right corner, with the 12 above it (refer to the above diagram).

The word jet breaks down into 6 and 1, which helps remind to place the 6 to the left of the 11, and the 1 just above the 6.

Tomatoes breaks down into 13 and 10, so the 13 goes just to the left of the 6, and the 10 goes just above 13.

Finally, sock (0 and 7) is a reminder to place the "0" (actually the empty square) in the bottom left corner, to the left of the 13, with the 7 directly over the empty space.

This may all sound confusing in text, but if you work through it with a 15 puzzle in front of you, it will help make everything much more clear.

As you work through these steps, it will also become simpler to remember which numbers are two-digit numbers, and which are single-digit numbers.

P.S.: On an unrelated note, this is the first post for this blog that was done by using the Dashblog widget.

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