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Broken Calculator (Posted on 2005-01-20) |
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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?
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Submitted by David Shin
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Rating: 3.6250 (8 votes)
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Solution:
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(Hide)
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For any nonzero u, one can compute u/2 by 1/(1/u+1/u). One can also compute u^2 for u not equal to 0 or 1 by u-1/(1/u+1/(1-u)). The product xy can then be computed by
((x+y)/2)^2-((x-y)/2)^2. |
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