Question of the Day #264 (24/5/10)

Kazza

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Using all of the following numbers once only, work out the following sum:

1 2 3 4 5 6

_ _ x _ = _ _ _



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I started by trial and error, but then I came up with a methodology that sped up the process. I'll post what I did tomorrow for you but I am also curious if there is an actual way to mathematically solve this.
 
Using all of the following numbers once only, work out the following sum:

1 2 3 4 5 6

_ _ x _ = _ _ _


The answer is
54 x 3 = 162
I don't know a quick way to work this out, for me it's trial and error!


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Here's what I did to solve it, though I'd still like a math wiz to tell me how to do it without trial and error. I just created an Excel table with all the possible multiplication combinations.

attachment.php


You can remove all of the numbers from the 1 column. You can remove any numbers that contain duplicate numbers. You can remove any numbers that have a "0", "7", "8", or "9". Once you establish the criteria, you can remove numbers pretty quickly and get it narrowed down. I found this way to be much quicker for me than just guessing and checking random numbers hoping to get it.
 
This is similar to the way I used too. I don't really think there is another mathematical way to calculate the answer.
 
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