If you don't immediately grasp what this sentence is asking you to do, don't despair - its actually quite easy to understand once you know exactly what the terms mean.

What is a 'bilateral ribbon'? The best way to understand what one is is to make one. Even if you do understand the meaning of the term, it is recommended that you make the ribbon, for it may be difficult to imagine a solution to the problem in the absence of an actual ribbon of this sort which can be physically manipulated.

Cut out a simple, rectangular strip of paper, like the one in the picture to the left, at the top. It should be about 20 inches long and 1/8 of an inch wide. The strip really needs to be that long since it has to be twisted a number of times. After you've cut out the strip, place it flat on a table in front of you. On the left end of the ribbon, mark an X, on the side facing you. Mark another X on the right end of the ribbon, also on the side facing you. Both Xs are, needless to say, on the same side of the ribbon - like in the picture.

In the picture you will also see a line going lengthwise up the middle of the ribbon; we will call that line the ribbon's 'lengthwise axis'. Now, while holding the left end of the ribbon stationary with your left hand, grasp the right end with your right hand. If with your right hand you twist the ribbon 180 degrees in a clockwise direction with respect to the lengthwise axis of the ribbon, what you get should resemble the bottom figure in the picture to the left. The X on the right hand side is no longer facing you. If you twist the ribbon clockwise 360 degrees - one full turn (not depicted in the picture) - the X on the right end should once again be facing you).

But instead of doing that, twist it TWO full turns (720 degrees) in a clockwise direction. Both Xs should again be facing you. Bring the two ends toward you, making a closed loop. Both Xs should now be facing AWAY from you. Overlap the ends slightly, and scotch tape them securely together. You should now have a closed circular bilateral ribbon; the ribbon wraps back on itself after making two full twists. This ribbon that you now hold in your hand can be transformed, without cutting or folding it, into a unilateral ribbon.

Such a configuration is called a 'bilateral ribbon', by the way, because the ribbon has two sides and two edges. You can prove this to yourself by placing the point of a pencil down somewhere on one side of the ribbon - without picking it up from the paper, run it lengthwise up the middle of the ribbon. You will eventually arrive at a point that is located approximately where you started. If, after having done that, you were to take the scotch tape off of the ribbon and spread the rectangular strip flat on the table. We don't recommend you do this now, as you need the ribbon to solve the puzzle. But if you did, you'd see that only ONE side of the strip has been marked by the pencil. There are no pencil marks on the other side. Similarly, if you were to use a magic marker to paint one edge of the closed circular bilateral ribbon, you'd see that there exists another edge - which is left unpainted.

If, in making the closed circular ribbon, you had originally twisted it only a half turn (180 degrees) or three half turns (540 degrees) or any ODD number of half turns, you would have created a UNILATERAL ribbon - a ribbon with only ONE side, and ONE edge. Had you run your pencil lengthwise up the middle of one side of this type of ribbon (which is sometimes called a 'mobius strip') and then untaped the ribbon and spread it out flat on the table, you'd have discovered that your pencil mark traversed BOTH sides of the strip of paper. Or, after painting along one edge of this unilateral ribbon with a magic marker, you would have discovered no second edge left unpainted.

So now you know what the difference is between a bilateral and unilateral ribbon. For the purpose of this puzzle, lets focus on the first configuration described above - the closed circular bilateral ribbon that you made by twisting the ribbon two full turns (720 degrees). Assuming that you have made such a figure, have it in front of you now, and are confident that the ends have been taped securely together, it is now time to try to solve the puzzle. Without cutting or tearing this bilateral ribbon in any way, or creating creases in it (by folding it), transform it into a closed circular unilateral ribbon.

This may not easy to do, but it can be done. You can find the answer to this puzzle in Saving Face.

If you are the type of individual who does not want to be told the answer, but might relent - when the going gets rough - to accepting a hint or two, check out the 'This Issue' section of the Journal - where a few have been artfully embedded.