From: rhinoceros (rhinoceros@freemail.gr)
Date: Fri May 21 2004 - 15:16:43 MDT
[rhinoceros]
I am reviving this thread for a reason. I stumbled on something exciting about the general question "how do we think when trying to solve a puzzle." It involves the evolutionary aspect of heuristics. (Ok, no need to comment on what gets me excited, i know :P )
While preparing a post with the stuff I found (maybe tomorrow), let me return to a couple of points from past posts.
(A)
<quote from a previous post of mine>
"Well, maybe I am just babbling and all this is not really necessary for solving the eight 8s puzzle. There is a way to know. Just solve the same problem with eight 8s giving a sum of 700 instead of 1000. I just made it up myself, so you can't google it. "
<end quote>
I saw no answer to how you can combine eight 8s to form the number 700, using only the eight 8s, the +-*/ signs and parentheses. If nobody finds an answer by tomorrow this is automatically declared a "TDCoV problem" (Too Difficult for the Church of Virus).
(B)
The last puzzle of this thread was the problem of the 10 divisions.
"Can you name the smallest number, which when divided by 10 gives a reminder of 9, when divided by 9 gives 8 as the reminder, when divided by 8 gives 7 as the remainder and so on, down to a remainder of 1 when divided by 2?"
That was perhaps the easiest of the 3 problems posted, but it poses an inetersting issue:
Solution 1: You write a trivial program to start from number 1 and check them sequentially one by one until it finds a number which does what we wanted. In a fraction of a second the computer arrives at the number 2519.
Solution 2: You notice that if you add 1 to the number you want it will be exactly divisible by all 10 numbers. So you construct that number by factoring-in the 10 numbers (2^3*3^3*5*7=2520), subtract 1 and find 2519.
Solution 2 requires some school knowledge, perception, and intuition. Solution 1 requires only a trivial technical competence and some equipment. However, Solution 2 gives me a sense of "satisfaction" while Solution 1 gives me a feeling that I didn't really understand "why" this was the answer. Can you offer any explanations for this feeling?
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