### Author Topic: ZT: 2、 3 、10、 10算24点，你能算出来吗？  (Read 10099 times)

#### 万精油

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• Posts: 1831
##### ZT: 2、 3 、10、 10算24点，你能算出来吗？
« on: 八月 08, 2011, 11:17:04 am »

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--万精油--

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5秒后，解法一出炉

2*（10-3）+10

2*10+3+log10

(10C3)*2/10

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（根号下10X10 —2）X3

（10+2）÷sin（3*10）

(10-2)*min(3,10) 噗第八
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« Last Edit: 八月 20, 2011, 12:01:03 pm by 万精油 »

#### 万精油

• Hero Member
• Posts: 1831
##### Re: ZT: 2、 3 、10、 10算24点，你能算出来吗？
« Reply #1 on: 八月 08, 2011, 11:23:17 am »

10+10+3!-2

(min(10,10)-2)*3

(max(10,10)-2)*3

(10+2)/cos(3!*10)

10+10+3+(2->)

(10-(3<-))+2*10

....

#### packman

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• Posts: 226
##### Re: ZT: 2、 3 、10、 10算24点，你能算出来吗？
« Reply #2 on: 八月 08, 2011, 11:05:09 pm »
My interpretations:

Min and max? Come on, that is cheating. You can ignore the rest numbers if you get 24 with only two or three numbers.
Trigs? Sin(3*10)? what is the unit of 3 or 10? Sqrt of degree?
Exponential is fine, just like multiplication. 2 * 3 is 2 added 3 times, as to 2^3 is 2 multiplied 3 times.
In the same token, square root  or other roots can be used only if it is expressed as ^(1/n). Log can be used only if the base is written out.
Factorial? No. It introduces extra numbers (5! introduces 1 thru 4).

#### fzy

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• Posts: 520
##### Re: ZT: 2、 3 、10、 10算24点，你能算出来吗？
« Reply #3 on: 八月 09, 2011, 02:18:43 pm »
This is an earlier IBM problem: Using two 2's and any common mathematical functions and operations, to obtain 5.

After some thoughts, I was able to extend it to this: Given two arbitrary rational numbers r1 and r2, using only the functions available on a calculator, ie, exp, ln, sin, cos, tan, arcsin, arccos, arctan, and - (unary negation), start from r1 and end at r2. For example, exp(0) = 1.

But as usual, I don't seem to remember how that was done.

#### 万精油

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##### Re: ZT: 2、 3 、10、 10算24点，你能算出来吗？
« Reply #4 on: 八月 09, 2011, 02:40:28 pm »
Quote
Given two arbitrary rational numbers r1 and r2, using only the functions available on a calculator,
ie, exp, ln, sin, cos, tan, arcsin, arccos, arctan, and - (unary negation), start from r1 and end at r2.
For example, exp(0) = 1.

Most calculators have the sqrt operator (e.g. the one that comes with Windows has sqrt).

Starting from any number, push sqrt enough times, you will get 1.

Most calculators have the feature that if you push +, the current number will be stored as the number
to be added, then push =, the sum of the current number and the stored number will be showing.
Keep push the = operator, the stored number will be added again and again. Thus, starting from 1,
you can get any number.

#### 万精油

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• Posts: 1831
##### Re: ZT: 2、 3 、10、 10算24点，你能算出来吗？
« Reply #5 on: 八月 09, 2011, 02:43:07 pm »
As a side note, a similar problem is, given four 4's, using the common operator (+,-,*,/, !, ^, sqrt), we can get every number from 1 to 72, I haven't been able to get 73.

If we have more discussion on this, I will move this to the puzzle forum.

#### fzy

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• Posts: 520
##### Re: ZT: 2、 3 、10、 10算24点，你能算出来吗？
« Reply #6 on: 八月 10, 2011, 04:55:28 pm »
Oh please! This is the last forum where most people are not stupid. I really wished I do not need to state all the necessary conditions as clearly as possible.

It is specifically stated in the IBM problem that using square root counted as using a 2, as well as using base 2 log.

Also the two sides need to be mathematically equal.

#### 万精油

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• Posts: 1831
##### Re: ZT: 2、 3 、10、 10算24点，你能算出来吗？
« Reply #7 on: 八月 20, 2011, 12:08:12 pm »
I almost missed this reply from fzy (due to the forum was having trouble for two days, and the reply was during those two days or immediately before it), just found out it today. And I think it is moving towards puzzle, so I moved the topic to this  forum.

Quote
Oh please! This is the last forum where most people are not stupid. I really wished I do not need to state all the necessary conditions as clearly as possible.

Since the topic was in humor, I gave a humorous answer. Obviously, it was not that funny.

Quote
It is specifically stated in the IBM problem that using square root counted as using a 2, as well as using base 2 log.

I don't remember seeing this problem in IBM problems. Now that we have moved this problem to here, can you gave a link of the IBM problem so that we know what is exactly the requirement (what are allowed and what are not). Thanks.

#### Dr Kevin Wang

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• Posts: 129
##### Re: ZT: 2、 3 、10、 10算24点，你能算出来吗？
« Reply #8 on: 八月 23, 2011, 02:08:11 pm »
As a side note, a similar problem is, given four 4's, using the common operator (+,-,*,/, !, ^, sqrt), we can get every number from 1 to 72, I haven't been able to get 73.
If the following is allowed: decimal point in front (.4), and repeat decimal (.4~ meaning .444444444....), then 73 is possible.

If log is allowed, every positive integer is possible:
n = -log_{sqrt{4}} log_{sqrt{4}} sqrt{sqrt{sqrt{..........sqrt{4*4}....}}}
where there are n+2 nested square roots.