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Learning Math Home
Patterns, Functions, and Algebra
 
Session 3 Part A Part B Part C Part D Part E Homework
 
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A B C D E
Homework

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Solutions for Session 3, Part B

See solutions for Problems: B1 | B2 | B3 | B4


Problem B1

a. 

The output is 12.

b. 

The output is 16.

c. 

For an input n, the algorithm performs n >> 2n >> 2n + 2 >> n + 1 >> n - 6 >> 4n - 24.

d. 

Knowing that the output is 4n - 24 means that we have to solve 4n - 24 = 28, an equation that is solved by n = 13. This means that the input must be 13.

e. 

The input is 14.

f. 

The input is 18.

g. 

The input is 15.

<< back to Problem B1


 

Problem B2

Working backwards from the end of the algorithm to the beginning will undo it. There are other strategies, such as writing equations for each of (d)-(g).

<< back to Problem B2


 

Problem B3

Algorithm B "undoes" everything that Algorithm A does.

 

Take the input (the output of Algorithm A) and

 

Divide it by 4

 

Add 7

 

Double it

 

Subtract 2

 

Halve that

 

There's your output (of Algorithm B)

<< back to Problem B3


 

Problem B4

Test it out. See if you can figure out why it works by thinking of the algorithms as driving directions. Where would you end up if someone gave you directions like Algorithms A and B, and asked you to do them both? In short, yes, they undo each other.

<< back to Problem B4


 

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