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A woman labels the squares of a very large chessboard 1 through 64. On each square k, the woman puts 2^k grains of rice. How many more grains of rice are placed on the 10th square than on the first 8 squares combined?

 Feb 18, 2019
 #1
avatar+321 
+3

We can solve this with patterns!

 

Notice how 2^2=2^1+2^0+1

2^3=2^2+2^1+2^0+1

Etc...

So this means The first k squares al added together is equal the the k+1 square - 1.

With this, the first 8 squares added together is 2^9-1 = 511, 2^10=1024, 1024-511=513

 Feb 18, 2019
 #2
avatar+102466 
+1

Good work Babada,

I did it using GP formula and I got just 1 different from you.

this is ok because it us up to our guest asker to look at our working and decide who is correct :)

 

 

\(2^1+2^2+ ....+2^8 = \frac{a(r^n-1)}{r-1}=\frac{2(2^8-1)}{2-1}=2^9-2\)

 

\(2^{10}-(2^9-2)\\ =2^{10}-2^9+2\\ =2^9*(2-1)+2\\ =2^9+2\\ =512+2\\ =514 \)

.
 Feb 18, 2019

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