Nice Area Problem (3)

Geometry Level 2

What is the difference between the Red area and the Blue area if the numbers shown are the areas of the squares accordingly?


The answer is 5.

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Hana Wehbi by Hana Wehbi , 51, USA

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2 solutions

Naren Bhandari
May 11, 2018

Now the difference of red area and blue area is D = ( R 1 + R 2 + R 3 + R 4 ) − B D = ( 1 − W 1 + 2 − W 2 + 3 − W 3 + 4 − W 4 ) − B D = 10 − ( W 1 + W 2 + W 3 + W 4 + B ) D = 10 − 5 = 5 D = \,(R_1+R_2+R_3+ R_4)-B \\ D = \,(1-W_1 + 2-W_2 +3-W_3 + 4-W_4)-B\\ D = 10-\,(W_1+W_2+W_3+W_4+B) \\ \boxed{D = 10 -5= 5}

Note : R n = n − W n R_n = n - W_n , where n ∈ Z + < 5 n\in\mathbb Z^+ < 5 .

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Hana Wehbi
May 10, 2018

The difference is: ( 1 − a + 2 − b + 3 − c + 4 − d ) − ( 5 − a − b − c − d ) = 10 − 5 = 5 . (1-a+2-b+3-c+4-d)-(5-a-b-c-d)=10-5= \boxed{5}.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

As the amount of overlap is not specified, we may be sure it is immaterial. Therefore assume no overlap (squares are disjoint).

Then total area of red squares is 4+3+2+1=10. Blue square area is 5. Difference is 5. QED

Steven Adler - 4 months, 2 weeks ago

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