This puzzle of mine will enable to test your ingenuity in solving problems quickly, applying all your previous experience to get the correct answer in minimal time.
Start your timer.
Imagine being interviewed for a job of your best dreams.
The letters in the equation below represent POSITIVE INTEGERS.
You are asked to provide the value of t as accurate as possible.
Free to use brains, paper, calculator, friends...
Given:
t^2=Sqrt(116^m+611^n+225^q)
Your answer:
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Time spent:.
Your comments:
Initially, for some reason, I mistook the plus signs for multiplication asterisks. It's an interesting problem that way, so I might as well post the solution to that different puzzle:
(just think of the + signs as *'s)
116^m+611^n+225^q needs to be a perfect 4th power.
116 = 2^2 * 29
611 = 13 * 47
225 = 3^2 * 5^2
No prime factor is common to any of the other coefficients, so the m, n and q have to do two things: each has to bring its own coefficient up to a power of 4 in each of its prime factors (except for prime factor 3--see the next sentence), and each has to incorporate the 4th power of the other coefficients' prime factors(same factor 3 caveat). Since there are 3 terms the power of 3 must be taken into consideration by making that only the third power in each term.
That way the whole of the parenthetical formula will be a power of 4:
2^4 * 29^4 * 13^4 * 47^4 * 3^4 * 5^4 = 79843920112708892010000
Its square root is 282566664900, so that is the RHS, and therefore the LHS or t^2.
So t is that number's square root: 531570.
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Posted by Charlie
on 2023-05-24 11:00:48 |
Not the solution
