China DOS Union

Comrade, it seems that among these 72 numbers, 8 numbers are repeated:

4730 5134 4828 4724 4720 4742 4760 4754
Do we only need to consider the other 64 numbers?!

It's not like that. For example: 4078 + 4078 + 4078 + 4052 + 4650 = 20936. If there are 3 4078s in test.txt, the above formula is allowed to appear.

This further increases the difficulty!

If only considering 64 non - repeating numbers, according to the calculation, at least 35 numbers are needed, and at most 37 numbers

This is an inevitable situation in practical applications. That is to say, if the code doesn't calculate the repeated numbers, it's just to practice everyone's hands, not to solve my problem. Please understand.

In fact, excluding the number of combined numbers between 35 and 37, according to the conventional method, the possible number of combinations is still an extremely large number.

It seems to take a lot of time, hehe, not tested

SETLOCAL ENABLEDELAYEDEXPANSION for /f %%i in (data.txt) do ( set /a a1+=1 set _data!a1!=%%i) for /l %%a in (1,3,%a1%) do ( set /a b=%%a+1 for /l %%b in (!b!,1,!b!) do ( set /a c=!b!+1 for /l %%c in (!c!,1,!c!) do ( set /a d=!c!+1 for /l %%d in (!d!,1,%a1%) do ( set /a z="1/(171780-!_data%%a!-!_data%%b!-!_data%%c!-!_data%%d!)"||echo !_data%%a!+!_data%%b!+!_data%%c!+!_data%%d!^=171780&&set /a _data%%a=0,_data%%b=0,_data%%c=0,_data%%d=0) ) ) ) set pause

[ Last edited by everest79 on 2007-3-2 at 06:33 PM ]

Oh, it turned out to be a four-digit number, I mistook it for a five-digit number

Can't write anymore, too much

Such a difficult question is finally posted. Oh~ I can't figure it out, looking forward to experts

Just a single math problem can kill a lot of brain cells, let alone designing an algorithm. -_-!

Sorted:
3800 3858 4072 4162 4168 4188 4238 4240 4262 4270 4272 4322 4324 4498 4520 4616 4632 4682 4684 4704 4710 4712 4720 4720 4724 4724 4730 4730 4732 4742 4742 4744 4746 4754 4754 4760 4760 4762 4770 4776 4782 4784 4792 4808 4816 4824 4826 4828 4828 4830 4838 4896 4942 4948 5008 5076 5104 5130 5134 5134 5150 5164 5168 5174 5194 5206 5218 5224 5234 5266 5282 5348


Sum of the largest 38 numbers
5348+5282+5266+5234+5224+5218+5206+5194+5174+5168+5164+5150+5134+5134+5130+5104+5076+5008+4948+4942+4896+4838+4830+4828+4828+4826+4824+4816+4808+4792+4784+4782+4776+4770+4762=175264

Sum of the smallest 39 numbers
3800+3858+4072+4162+4168+4188+4238+4240+4262+4270+4272+4322+4324+4498+4520+4616+4632+4682+4684+4704+4710+4712+4720+4720+4724+4724+4730+4730+4732+4742+4742+4744+4746+4754+4754+4760+4760+4762+4770=176548>171780
Then what does this indicate? It can only be 38 digits. (I casually calculated that the sum of the smallest 38 is 171778)


Thus, the number of digits is limited! The number of operations is reduced from 2^72 - 1 to 396561735952215036840 times, which is approximately 344 * 2^60 times... Although it is very large, you should know that 2^72 is about 11.9 times of it!
And the number of operations can be further reduced...

The sum of the smallest 38 numbers has a difference of 2 from the required number (171780 - 171778 = 2)

3800 + 3858 + 4072 + 4162 + 4168 + 4188 + 4238 + 4240 + 4262 + 4270 + 4272 + 4322 + 4324 + 4498 + 4520 + 4616 + 4632 + 4682 + 4684 + 4704 + 4710 + 4712 + 4720 + 4720 + 4724 + 4724 + 4730 + 4730 + 4732 + 4742 + 4742 + 4744 + 4746 + 4754 + 4754 + 4760 + 4760 + 4762

And the 39th number is 4770. The number closest to it is the 38th one (I sorted them in order). And this number 4762 has a difference from 4770 that is greater than 2.

That is to say, if 39 is replaced with 38, the number becomes larger by 6 (171786). And this number is the 2nd smallest number among the 38 numbers. All the subsequent numbers are larger than it!

So the final answer comes out!!!!!

No qualifying combination

re slore
There won't be no qualifying combinations as you said, because I got this result after a selection and then made the question.

Originally posted by ccwan at 2007-3-3 08:49:
re slore
There won't be no combination that meets the requirements as I got this result after a selection, and then made the question.

Is your number 38?

Send me the short message with your number.
I think the analysis is not wrong... It won't be a calculation issue~

Sorry,Irandomlyselectedsomenumbers,gotaresultandsentitout,withoutrecordingwhichnumberstheywere,buttheremustbesuchcombinations.

Ifduetomyoversighttherereallyaren'tany,youcandefineoneyourselfaslongasitworks.