找规律

husonghu · 发表于 2006-11-26 00:54:44

A certain logic has been foolwed for the following groups of numbers. Complete the last one suing the same logic.

5____8______39

-2___6______12

15___2______51

7____7______?

那些花儿 · 发表于 2006-11-26 04:34:54

42？前两个数字加起来乘以3？

husonghu · 发表于 2006-11-26 04:46:24

很高兴看到花儿

那些花儿 · 发表于 2006-11-26 05:02:55

经常缺席，不好意思

bill · 发表于 2006-11-26 09:39:06

42

yinyin · 发表于 2006-11-26 11:31:55

Such kind of problems are insignificant if the reqired answer is a "number" but not an "integer" necessarily. There are infinitely many solutions for the given problem. For example, solving the system of linear equations: 25a+5b+8c+d=39, 4a-2b+6c+d=12, 225a+15b+2c+d=51 to get infinitely many solutions of (a, b, c, d), the answer of the given problem can be expressed as 49a+7b+7c+d. Your answer is just a particular solution b=c=3 and a=d=0 among those infinitely many solutions. Even if the answer is required to be an integer, it is still possible to find another answer when we use higher order polynomials or other types of functions to form the system of equationa (may not be linear). Of caurse, the "logical rules" may be very complex.

husonghu · 发表于 2006-11-26 12:02:51

这里答案确实是唯一的: 42。你能给个其它答案试试看？

yinyin · 发表于 2006-11-26 13:35:18

Your answer is a particular solution when a=0. However, for any chosen non-zero real value as a, you can get another particular solution. For example, taking a=1, you can obtain b=-9350/1705, c=7568/341, d=-4220/31, and the answer of the problem is 50875/1705.

The corresponding logical rule is: a(x1)^2+b(x1)+c(x2)+d, where x1 and x2 are the first two numbers in each given condition, respectively. Please verify that the above example satisfies your three conditions. Generally (except some degenerate cases), the logical rule can be chosen from any kind of functions of x1 and x2 with more than 2 unknown parameters (they can be determined by the conditions) to get solutions of your problem. When you give n conditions, the number of parameters in the function should be at least n.

husonghu · 发表于 2006-11-27 00:35:37

我想，尽管没有说，原题中还是隐含其它条件的。

首先，“答案的形式”就是规律之一。答案的形式应与给的例子一样：例子是integer，答案就应也是integer，否则就违反了规律；其次，作为IQ题，即便有符合规律的多重答案，答上一个就是答对了(应是最简的)。

不过你们的观点从数学上说很对，使人长知识了。我开始时没想到这一层。

yinyin · 发表于 2006-11-27 11:20:33

"例子一样" has not been defined. For example, if the right-hand side in all examples is an even number (or greater than some given number, or divisible by 5, ...), should the answer also be even (or greater than the given number, or divisible by 5, ..., respectively)? Also, "最简的"

has not been well defined. www.ddhw.com

I have another example that is helpful to understand the essence of the problem: "If the first three terms of a sequence is 1, 2, 4, what is the fourth term logically?"

Such kinds of “IQ” problems are very easy to be constructed. Even a premier school student can construct one hundred of such kind problems within one hour. www.ddhw.com

As for your proposed problem, an additional condition "according to a logical rule expressed by a linear function" should be included to guarantee the uniqueness of the answer.

xlxk · 发表于 2006-11-27 22:21:55

I personally hate this kinds of problems. One can actually fill in any numbers by building models with sufficiently many variables.

husonghu · 发表于 2006-11-28 02:24:27

Right!

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找规律

喜欢7这个数字，所以努力想了...[:-M]

[:-Q][:-Q]很高兴看到花儿[@};-][@};-]

[>:D<]经常缺席，不好意思[:>]

回复：找规律

回复：找规律

yinyin啊，不懂你所讲的。好象你搞得复杂化了。哪来什么a，d？什么higher order？..

回复：yinyin啊，不懂你所讲的。好象你搞得复杂化了。哪来什么a，d？什么higher order

懂了俩位说的。俩位是按数学题来做了。但这是IQ题。IQ test 里见很多这种题.....

回复：懂了俩位说的。俩位是按数学题来做了。但这是IQ题。IQ test 里见很多这种题.....

回复：找规律

[:-Q][:-Q]Right!