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Broken Calculator (Posted on 2005-01-20) Difficulty: 3 of 5
You have a calculator whose multiplication button is broken. The only operations that work are addition (x+y), subtraction (x-y), and reciprocation (1/x).

Can you use this calculator to multiply two numbers?

See The Solution Submitted by David Shin    
Rating: 3.6250 (8 votes)

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Solution to this problem. | Comment 10 of 14 |

Let us assume that we want to multiply two numbers x and y.

That means we need the value of  xy ( x multiplied by y).

We already had operations for finding reciprocal (1/x or 1/y) , Addition x+y and subtraction x-y etc, but not mulitiplication button on the calculator.

Here are the steps I perform for calculation of xy.

First I will evaluate 1/x and keep the value in memory.

Then I will calculate (1/x)+y which is equal to (1+xy)/x.

Then I will divide this value with the value in memory that is 1/x which gives me 1+xy on display.

Now as I had a workable substraction button on my calculator I will substract 1(one) from the value on display(1+xy) which gives me the value of xy.

That is the required answer to this problem as I got xy without using mulitiplication button but using division,addition and substraction.

 


  Posted by Pemmadu Raghu Ramaiah on 2005-01-21 12:25:20
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