From: rhinoceros (rhinoceros@freemail.gr)
Date: Fri Feb 27 2004 - 17:50:31 MST
[Mermaid]
hey! the rhino is still alive...
[rhinoceros]
Yes, he is. But... having to deal with my own shit over here, it took a good bait such as this thread to make me post something :P
[Mermaid]
ok..here is another one..how do you 'arrive' at the solution...
"can you combine eight 8s with any other mathematical symbols except numbers to represent exactly 1000? you may use addition, subtraction, multiplication, division signs."
everyone probably knows the answer to this too...these are one of the more popular puzzles...but how do you train your mind to 'arrive' at the solution...its one thing to keep reading it over and over until you can recite it as a party trick to impress..and totally another when the solution and the way to the solution looks clear...it feels as though i am missing out on a 'way of thinking'...of problem solving...
[rhinoceros]
I didn't know the answer to this one. After one hour of fruitless efforts I had to google it (the answer is the deceivingly simple 888+88+8+8).
It seems incredibly difficult to find the answer in a straightforward way. You have to try to find a particular combination of arithmetic operations (additions, subtractions, multiplications, divisions) acting not only on (combinations of) 8s but also on 88s (=8*10+8) and 888s (=8*10^2+8*10+8). A computer program would have to use a heuristic tree search, applying some kind of "forward pruning" to the "not promising" branches (for example, when you examine an addition of numbers ending in 8, as is the case with the solution, you only examine additions of 5 terms so that the result ends in 0).
If I am not missing something from maths, this seems to be a problem where a human would have to "think like a computer" (unlike the towers problem). However, this was also true for many other problems, which seem easy today with the mathematical tools we have developed (like the towers problem).
So, my best answer to the question "How do you find it" is "Make smart guesses, take shortcuts wherever possible (familiarity with number theory helps here), and take your time..." It seems good for practicing your associative reasoning (your intuition, if you prefer.) A computer is quite good at this kind of problems, since there is a huge literature on smart heuristic searches.
[Mermaid]
also...do we really use algebra in our everyday lives? really..do we?
[rhinoceros]
Some never do, some do and find a few uses for it, and some do and find a lot of uses for it. There is also a rumor about some weirdos using calculus in their everyday lives, but I can only confirm that some use probability theory. :P
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