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Choosing correct variables

This week, we learn about Choosing correct variables. By expressing our ideas using the appropriate variables, which may not have been highlighted in the question, we can simplify the problem which makes it easier to understand and approach it.

What question would you use to illustrate how the technique of Choosing the Correct Variables can be very useful to interpreting a problem? Just state the problem, and leave it to others to work out the approach.

Note by Calvin Lin
3 years, 10 months ago

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I got stumped on this week’s question Rooted Away, and it seems to use very similar concepts. It asks you to solve

\[ x = \sqrt{4-x}\sqrt{5-x} + \sqrt{5-x}\sqrt{6-x} + \sqrt{6-x}\sqrt{4-x}. \]

When I first worked on it, I couldn’t get anywhere, and didn’t want to square all the ugly stuff.

I got impatient, entered the solution discussion, and read C L ‘s solution. It's amazing how much his choice of variables simplified the problem!

P.S. Is C L a nickname for Calvin Lin? Michael Pedersen · 3 years, 10 months ago

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In a street , there are more than thirty but less than seven hundred houses in a row , numbered from 0 , 1 , 2 , 3 etc . consecutively . There is a house in the street , the sum of all the house numbers on the left side of which is equal to the sum of all house numbers on its right side . Find the house number . Santanu Banerjee · 3 years, 10 months ago

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