taking the help of the hall) - page 6

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Integer:

Please:

319,319,662,460,383,662,552,552,319,107,319,154,10,25,10,222,460,185,266,662,319,460,107,185,222

Indeed:

319+319+662+460+383+662+552+552+319+107+319+154+10+25+10+222+460+185+266+662+319+460+107+185+222 =7941

But I have a different set of numbers. Any other options?

 

The TOR is still extremely vague and is now very different from the original one.

I initially understood the problem this way: there is a vector a = (10, 12, 14, 17, 21, 25, 30, 36, 43, 52, 62, 74, 89, 107, 128, 154, 185, 222, 266, 319, 383, 460, 552, 662, 795, 954, 1145, 1374, 1648, 1978) in 30-dimensional space.

Find all vectors b in the same space - such that ( a, b ) = H.

The components of vector b can only be integers 0 or 1. The number H is given beforehand.

For this problem I cannot offer anything but a blind search.

If you need to find one partial solution, Excel is at your disposal.

 
Mathemat:

The ToR is still extremely vague and is now very different from the original one.

I initially understood the problem this way: there is vector a = (10, 12, 14, 17, 21, 25, 30, 36, 43, 52, 62, 74, 89, 107, 128, 154, 185, 222, 266, 319, 383, 460, 552, 662, 795, 954, 1145, 1374, 1648, 1978) in 30-dimensional space.

Find all vectors b in the same space - such that ( a, b ) = H.

Only integers 0 or 1 can be components of vector b . The number H is given beforehand.

For this problem I cannot offer anything but a blind search.

If you need to find one partial solution, Excel is at your disposal.

Oooh, so I'm not the only one who didn't understand the assignment. So, topicstarter, shall we revise the assignment or keep the one on the previous page?
 

Mathemat, don't make it harder)

joo , here's another way of solving your problem : 222+266+128+107+128+154+30+460+383+552+222+266+128+107+128+154+43+460+383+552+1978+25+74+662+222+107

 
joo:

Indeed:

319+319+662+460+383+662+552+552+319+107+319+154+10+25+10+222+460+185+266+662+319+460+107+185+222 =7941

But I have a different set of numbers. Any other options?


I think there are, but I'm not an ironclad machine looking for all the options)
 
vitali_yv:

Mathemat, don't complicate it.)

joo , here's another version of your problem : 222+266+128+107+128+154+30+460+383+552+222+266+128+107+128+154+43+460+383+552+1978+25+74+662+222+107

The problem doesn't get any more complicated, just the condition changes.

So what should I do? Show me the solution to my problem, your last one, or Alexei's?

 
Mine, if you don't mind.
 

Well then another question: can it only be sums with positive coefficients - or any linear combinations with integer coefficients?

For example, 134 = 3*222 - 2*266.

 
If we are talking about linear combinations, the coefficient should be one - 1. In other words, it's not the coefficients, but the elements of the vectors that form a given sum.
 
So I got the problem absolutely right from the start (see the same page)? In other words - no repetitions: each number is involved either once, or it is not in the sum. Right, Vitaly?
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