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Katy
Junior Member

Canada
6 Posts

Posted - 09/25/2009 :  19:44:38  Show Profile  Reply with Quote
A number magician tells you: Pick any postive integre and mutiply it by 18. Delete one of the non-zero digits of the poduct.Tell me the sum of the remaning digits of the product and I will tell you what digit you deleted.Explainthis trick.
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Katy
Junior Member

Canada
6 Posts

Posted - 09/25/2009 :  19:52:33  Show Profile  Reply with Quote
Any help is greatly appreciated this is kinda urgent
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anonmeans
Senior Member

USA
37 Posts

Posted - 09/27/2009 :  08:30:08  Show Profile  Reply with Quote
Pick a variable for the unknown number. Create expressions representing what you're doing to the number. Simplify. See what you get.

If you get stuck, please reply with your steps and reasoning, starting with your variable and the expression you got after multiplying by 18.
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Subhotosh Khan
Advanced Member

USA
9117 Posts

Posted - 09/28/2009 :  09:52:57  Show Profile  Reply with Quote
quote:
Originally posted by Katy

A number magician tells you: Pick any postive integre and mutiply it by 18. Delete one of the non-zero digits of the poduct.Tell me the sum of the remaning digits of the product and I will tell you what digit you deleted.Explainthis trick.



Any multiple of 9 will have a sum of digit that is divisible 9.

18 is divisible by 9.

So when you are looking at multiple of 18 - it is a multiple of 9 too.

Thus multiple of 18 will have "sum of digits" divisible by 9.

suppose you chose 18 * 43 = 774

and you decide to drop 4 - so sum of remainig digit is 14.

You must have started from a sum-of-digit of 18 - so you must have dropped 4.

Try other numbers say 18 * 69 = 1242

You decide to drop '4' and give me the sum '5'

You must have started from '9' and you have dropped '4' (= 9-5)
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