## Right From Left

EDMUND ROWLAND

IT ISN'T often that one comes across a mathematical effect which lends itself to comedy, but here is an amusing item which can be used in almost any kind of show. It is quite impromptu and requires no amount of preperation at all.

A number is written on a slate, and someone is asked to divide it by any number which he cares to think of between 5 and 10, and to concentrate upon the remainder. Although you cannot possibly know the number he has chosen, you promise to reveal the remainder in a rather novel way.

As he is busily working out the division you pick up a rectangular piece of plain paper, fold it twice in half (from top to bottom, and from side to side), and then proceed to tear it as shown in the first illustration. Instead of dropping the pieces on to your table or the floor, they are given to another spectator to hold. The reason for this will be obvious in a moment.

When the pattern which you have torn is half opened out, the result is a figure 0, as shown in the second illustration, and this you announce as the number on which the spectator is concentrating. But wait a moment. He is shaking his head, and even beginning to smile, as if you have made a mistake. " I'm sorry," you say. " Isn't that the number you are thinking of? Oh yes, of course; I haven't opened the paper out completely." As you are saying this you open it out to form a figure 8, as shown in the third illustration. But the spectator is still shaking his head, and probably laughing at you. With some apparent embarrassment, for you have really been caught this time, you fold the figure in half down the centre to form a figure 3, as shown in the fourth illustration. But even this is wrong, and by this time most of the audience are amused. The only thing that you can do is to throw the paper away and go on to something else. " There doesn't seem to be anything else left," you say.

The mention of there being anything left, however, seems to suggest a way out of your predicament. " I really am being careless, aren't I? I seem to be forgetting what I am doing. I'm supposed to be telling you what you had left when you had finished the division. So let me see what I had left when I had finished my little bit of paper tearing."

You immediately turn to the spectator who has been holding the torn pieces and you ask him to open them out and count them carefully on to your hand. He does this very willingly (because he has been wondering what he was supposed to do with them), and finds that there are four separate pieces, as shown in the fifth illustration.

And now it appears that you are finally correct, for the first spectator turns the slate to show that this was the actual remainder to the sum. In the final round of laughter and applause (?) which follows, you collect your slate (and the piece of chalk) and proceed to your next effect.

The secret is simply that the number which you write on the slate is 508 because the remainder when this is divided by 6, 7, 8 or 9 is always 4 and cannot be anything else. The paper-tearing really works itself, so unless you have been unlucky enough to pick on someone who is quite hopeless at arithmetic, you have nothing at all to worry about.

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