#Solving magic square style puzzle with matrices?

16 messages · Page 1 of 1 (latest)

inner tundra
#

The cells must be filled with integers in {1,2,...,12} and they must all be distinct. The numbers on the outside indicate the sum of the cells. For example, the 1st row's cells sum to 18, and the 2nd column's cells (8,12,11) sum to 31.

My Background: I have my university entrance exam tomorrow (computer sci). This type of question might come up in it. I only have a basic calculator in the test with me. I can solve these types of puzzles given enough time (in like an hour, which might be too long in an exam with lots of questions) using trial and error and some logic. I'm familiar with systems of equations and I know the concept of matrices. I've heard that using linear algebra, these puzzles can be solved on pen and paper more systematically than with trial and error. I'm wondering if I should learn that technique in case this type of puzzle comes up in the test.

Question:
Can I learn the linear algebra technique in a few hours, today? Or should I just go with my current technique and practice other topics as well today?

bc9674173ed336f01921597408a557c6.webp
inner muskBOT
#
  1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
  2. Wait patiently for a helper to come along.
  3. Once someone helps you, say thank you and close the thread with:
    +close
  4. Feel free to nominate the person for helper of the week in #helper-nominations
  5. Do not ping the mods, unless someone is breaking the rules.
  6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:
wintry fjord
#

I don't think this has an answer

autumn merlin
#

it has an answer

#

i hope the OP did well on their exam

#

lemme refind the ans

wintry fjord
#

Wait, I thought the sum of the collumns =/= sum of the rows

autumn merlin
#

||1 8 3 6
5 12 7 9
2 11 4 10||

wintry fjord
autumn merlin
# wintry fjord I'm curious what method you used?

well i ignore the given column so just subtract it out
we need to organize 1 2 3 4 5 6 7 9 10, first column should be 134 or 125, the last column must be 6 9 10, then with each possible column distribution i found 3 that add to 10 (=18-8) , from here its quite easy just guess and check

wintry fjord
autumn merlin
#

this table is highly underspecifief *underdetermined

#

the requirement of 1 through 12 each once is necessary

#

and i don’t know of any way to get that information into an equation

#

plus, this method doesn’t require working with a 9x9 matrix or whatever