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Topic: One in thirteen (Read 425 times) |
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pcbouhid
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One in thirteen
« on: Nov 26th, 2005, 5:19am » |
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One of the thirteen numbers below, all written with all the digits from 1-9, has something special when compared to the other twelve. What is the number and what makes it "different" from the others?
164,729,835 / 231,498,675 / 248,136,975 / 248,316,975 / 248,361,975 /
321,498,765 / 326,498,715 / 328,496,715 / 347,182,965 / 348,271,965 /
632,971,845 / 736,981,245 / 812,973,645
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towr
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Re: One in thirteen
« Reply #1 on: Nov 26th, 2005, 1:45pm » |
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They all have something special.. Otherwise there would be a least non-special one, which makes it special. 
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pcbouhid
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Re: One in thirteen
« Reply #2 on: Nov 27th, 2005, 4:13am » |
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Itīs a good point. But, what if you divide each of them by the sum (the same) of their digits?
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towr
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Re: One in thirteen
« Reply #3 on: Nov 27th, 2005, 8:02am » |
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Certainly interesting, but it doesn't help to decide which special trait you might be looking for.
when divided by 45, they're all palindromes.
One is the only one to have 3 5 in the middle. One is the only one to have a 0 in the middle. One is the only one to have 1 but not 3 fours in the middle. For one all digits are divisible by 3, etc.
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BNC
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Re: One in thirteen
« Reply #4 on: Nov 27th, 2005, 8:49am » |
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My two favorites are:
164729835 (dividing by the sum of the digits yields another palindrome (ignoring the decimal point)).
328496715 (the sum of the resulting palindrome is 45 again).
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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pcbouhid
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Re: One in thirteen
« Reply #5 on: Nov 27th, 2005, 1:15pm » |
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The "special" number is 347,182,965, that divided by 45, gives 7715177, the unique ............. among the thirteen quotients.
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pcbouhid
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Re: One in thirteen
« Reply #7 on: Nov 27th, 2005, 1:49pm » |
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Agree with you. Should you move this one to the "hard" section?
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JocK
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Re: One in thirteen
« Reply #8 on: Nov 27th, 2005, 2:14pm » |
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on Nov 27th, 2005, 1:49pm, pcbouhid wrote:| Agree with you. Should you move this one to the "hard" section? |
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I think what makes this problem difficult to tackle is the fact that there is simply not enough information. As a result, there is lack of 'direction' for finding a solution.
Yet, such ambiguous problems hardly ever constitute true 'hard' problems. The best 'hard' problems are those that are easy to state, leave no room for interpretation, and despite that are hard to solve...
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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towr
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Re: One in thirteen
« Reply #9 on: Nov 27th, 2005, 2:58pm » |
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This is a little bit like a "guess what I'm thinking"-riddle.
Although in the end it does turn out to be a rather fundamental property you're looking for; and much better than our suggestions. 
As for what sort of puzzles belong in the 'hard' fsection, Jock says it quite well.
Another criterion might be that the answer for a 'hard' puzzle doesn't in any way solve it. Having the problem and the answer won't make it much easier to find the solution than not having the answer.
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pcbouhid
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Re: One in thirteen
« Reply #10 on: Nov 28th, 2005, 11:57am » |
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Agree with all your comments. In fact, I submitted this "problem" because I saw it once in a site.
And you are right when say "this is a little bit like a "guess what I'm thinking"-riddle.""
Itīs like: "whatīs the next term in this sequence ; 1, 2, 3, ...". Could be a lot of numbers, starting with 4, or 5, etc... depending on "what I am thinking".
In short, thereīs no sufficient information to guide to a reasonable solution.
Iīll try to avoid this kind of puzzle.
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Icarus
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Re: One in thirteen
« Reply #11 on: Nov 28th, 2005, 3:31pm » |
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I won't say that "Guess what I am thinking" puzzles should always be avoided - there are some that are quite insightful.
My preference in puzzles is for those which provide all the information the solver needs to deduce a unique solution (or description of all solutions) within the problem statement, but which require insight or unusual reasoning to make the deduction. (For example, your "Red Discs" puzzle, which requires the solver to consider cases he already knows are false to solve it.)
Unfortunately, though, most puzzles at all degrees of difficulty fall short of this standard. Some only a little, others more. However, if they still require some twist of reasoning to solve, and include enough information to point the solver in the right direction, I still find them enlightening, and enjoy them.
The problems I don't enjoy are those that simply require tedious slogging along well-worn paths to eventually grind an answer out (for example, problems that must be solved by much trial and error), or those that require a lot of guessing ("I'm thinking of a number. What is it?")
While this puzzle falls far short of the good criteria, it is not so bad as to meet the bad one.
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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