August Challenge of the Month Discussion

[Chris Davison]

How Many are the solutions?

Does Anybody knows ?

that's the challenge. How many are there, and list them.

 

[Jeffrey Chin]

Hi all,

this is my attempt to the "Holy Grail" challenge.. being a practical person, i prefer a quick fix to the problem to an academic approach.. my attempt is not a "find all solutions" method (i'll leave that to the academics) but a solution which is a quick fix to the accounts receivable department problem which took me about 2 hours.. here goes..

you may think it is crazy to randomly pick numbers fro the list to add up to 4556.92.. but this method is easy and it produces millions of guesses in a short time.. however, i hv an added twist to this (if not, you'll take forever to find just one solution).. i hv decided on a "half-guess half-calculate" method..

i will call the list of 54 (or 53) given numbers the universal set and the a list of numbers that add up to 4556.92 the solution set..

first, i produce a list of added pairs of numbers from the universal set.. this is because i know for sure that a potential solution set will have at least 2 numbers (any 2).. 53 numbers will give 1378 combination of added pairs.. you can derive this manually, which is not too difficult or write a simple macro for this.. i did manually..

second, i generate a potential solution set by randomly picking numbers from the universal set, taking the difference of the numbers with 4556.92 and comparing the difference with the list of added pairs to get 4556.92.. that is to say, the sum of randomly picked numbers plus an added pair = 4556.92.

you may say this is really weird.. but who cares, so long as it works and i can produce the solution for the accounts dept in 2 hours! (being practical).. well, the reason for producing the added pairs is to drastically reduce the guessing time for a solution set by greatly increasing the probability of a perfect match.. each solution set takes less than 30 seconds to run..

i hv problems attaching my spreadsheet and macro (can someone show me?).. anyway, these are some of my solutions using the above method..
185.58
194.58
222.52
228.31
230.72
630.92
1,021.70
1,842.59

630.92
144.77
324.84
515.11
538.64
628.89
789.77
983.98

89.40
126.69
160.62
280.71
698.27
718.32
895.39
1,587.52

409.17
722.73
858.97
978.53
1,587.52

77.74
192.65
222.52
346.35
507.08
722.73
2,487.85


440.93
444.98
456.68
673.47
698.27
1,842.59

 

[IOANNIS]

..that's the challenge. How many are there, and list them...

.. After a few modifications on my macro i realise that the total solution are too many ..

until now 295242 solutions

6000 to 17000 sol/hour

PAIR STATISTICS

TOTAL 295.242
01.02 144.682
01.03 78.894
01.04 42.585
01.05 23.701
01.06 5.380

.. 01 is the first number
.. 02 is the second
and so on
.. the numbers are sorted ascending


(I think that my english is not too bad ...)

 

[IOANNIS]

to Jeffrey Chin
You find solutions (randomly) because the total solutions of spesific sum are millions

what about 1546.66 which has only 19 in the same compinations with 4556.92

..i found all (19) in less than 30 sec ..

 

[Smiffy]

To Jeffrey Chin

And how long will it take if there are no matches ?

 

[Jeffrey Chin]

Hi IOANNIS

i donno if im lucky or wat.. as i said my method is not a "find all solutions" method but im able to find at least 3 solutions in to 1546.66 in giffy..
116.14
244.22
324.84
346.35
515.11

77.74
192.65
222.52
515.11
538.64

77.74
116.14
160.62
280.71
911.45

btw, i donno if there are 19 solutions for 1556.66 becos i threw away some like
83.06
346.35
440.93
329.97
346.35
where 346.35 is repeated.. cld u verify the 19 solutions pls.. same for 4556.92, i find it hard to believe there are hundred and thousands of solutions..

Hi Smiffy,

my macro runs forever if there is no match.. i guess i can put a stop to say 100,000 guesses if i want.. like i said, for this quick fix method for the accounts dept, i think they wld be happy to take say 10 solutions to start making phone calls!

well guys,
i'll try if i hv a brute force method to find all solutions..

 

[IOANNIS]

TOTAL SOLUTIONS OFF 4556.92

712473 ONLY !!!

..(If the macro has no bugs)

 

[IOANNIS]

TOTAL SOLUTIONS OFF 4556.92

712473 ONLY !!!

..(If the macro has no bugs)

 

[IOANNIS]

AUGUST_2002_53_02.xls
	B	C	D	E
4		FIRSTNo	SOLUTIONS
5	01	77,74	322.151
6	02	83,60	175.825
7	03	89,40	95.992
8	04	116,14	51.315
9	05	126,69	28.659
10	06	144,77	16.142
11	07	160,62	9.071
12	08	185,58	5.407
13	09	192,65	3.151
14	10	194,58	1.917
15	11	219,10	1.123
16	12	222,52	664
17	13	228,31	444
18	14	230,72	208
19	15	244,22	146
20	16	280,71	100
21	17	324,84	48
22	18	329,17	37
23	19	329,97	17
24	20	346,35	17
25	21	365,43	18
26	22	409,17	9
27	23	440,93	9
28	24	441,43	1
29	25	444,98	0
30	26	456,68	1
31	27	507,80	0
32	28	515,11	0
33	29	538,64	0
34	30	542,12	0
35	31	589,18	0
36	32	628,89	1
37		TOTAL	712.473
C_08_2000_STAT_54

 

[Jeffrey Chin]

Hi Ioannis

wat does the table mean?
does it mean the number 77.74 appears in 322,151 times out of all the 712,473 solutions?