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?
Any given number (n, say) can be divided by 2 in the following manner:
n/2 = 1/(1/n + 1/n)........(i)
Any given number (m, say) can be squared by way of the following
m^2 = m + 1/(1/(m-1) - 1/m) ..........(ii)
The product of two given numbers P and Q can be calculated in
the following way:
(P+Q)^2 - P^2 - Q^2 (Rule (ii))
-> 2PQ/2 = PQ (Rule (i))
*** Nice Problem
Edited on April 5, 2007, 11:34 am