How Does the Trick Work?Date: 06/20/2003 at 01:28:59 From: Ros Subject: Mathematics Patterns/Tricks Dr. Math, From time to time I've run across math tricks that ask me to give a number, then take me through a series of other questions and by the time I work my way to the end, the trick tells me my original number. How does this work? Date: 06/20/2003 at 13:04:27 From: Doctor Peterson Subject: Re: Mathematics Patterns/Tricks Hi, Ros. Here is an example of such a trick: Birthday Number Puzzle Variations http://mathforum.org/library/drmath/view/61702.html As you'll see there, you can see how the trick works by doing it not with a specific number, but with a variable. Then you find that all that is being done undoes itself in the end; the expression you are evaluating simplifies down to "x". It wouldn't look like much of a trick if I said this: Pick a number Multiply it by 7 Divide that by 7 Ta-dah! You've got your number back! It looks just a little more impressive if I say: Pick a number Multiply it by 7 Add 35 to that Subtract 35 from that Divide that by 7 Ta-dah! You've got your number back! You can still see that you are just undoing each thing you did. But it I tangle up this expression, (((x * 7) + 35) - 35) / 7 by instead doing this: (((x + 5) * 7) - 35) / 7 which means just the same thing, but doesn't have you both adding and subtracting 35, then it starts to look surprising: Pick a number Add 5 to it Multiply that by 7 Subtract 35 from that Divide that by 7 Ta-dah! You've got your number back! If I did a little more to twist it up, you'd never guess the outcome! All these tricks do is to hide the fact that you are undoing everything you did. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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