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PostPosted: Wed Apr 18, 2018 1:55 pm 
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Joined: Mon Oct 03, 2016 7:41 am
Posts: 6
circle + triangle = square
square + square = hexagon
circle + circle+ triangle = hexagon
what is the value of triangle? if all the shapes are numbers


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PostPosted: Wed Apr 18, 2018 2:01 pm 
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Joined: Mon Feb 12, 2007 1:21 pm
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idl wrote:
circle + triangle = square
square + square = hexagon
circle + circle+ triangle = hexagon
what is the value of triangle? if all the shapes are numbers


Replace square in second statement by circle + triangle.

circle + triangle + circle + triangle = hexagon

Then compare to third statement. Can you see the answer now?


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PostPosted: Wed Apr 18, 2018 3:52 pm 
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Joined: Mon Jan 24, 2011 4:33 pm
Posts: 950
It's the same problem as Bananaperson's thread entitled 'Help'. My solution is below but Guest55's is better because it's more straightforward.

Since circle+triangle=square, you can substitute a square in place of (circle+triangle) in line 3 to give circle+square=hexagon.

From line 2, you can then deduce that circle=square because we now have circle+square=hexagon in line 3 as well as square+square=hexagon in line 2. In other words, adding a circle to a square has the same effect (resulting in a hexagon) as adding a square to a square.

From line 1, now we know that circle=square, that must mean that triangle=0 because adding triangle to a circle doesn't change its value.

(which means that circle=1, square=1 and hexagon=2)


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PostPosted: Wed Apr 18, 2018 6:15 pm 
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Joined: Mon Oct 03, 2016 7:41 am
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hi ..
Thanks a lot both of you.
I worked out the ans as triangle =0 from many approaches but couldn't convince myself if circle and square have the same value.
Ofcourse the question doesn't say they are given different numbers so...it should be correct.

Thanks again.


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PostPosted: Wed Apr 18, 2018 7:26 pm 
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anotherdad wrote:
(which means that circle=1, square=1 and hexagon=2)


I think there will be a whole family of solutions? circle = square = n and hexagon = 2n


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PostPosted: Thu Apr 19, 2018 1:06 pm 
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Joined: Fri Mar 10, 2017 4:06 pm
Posts: 412
Yes I agree.

Triangle has to equal zero but circle and square can equal any number. (and hexagon can equal any number times 2)


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