Empty Boxes Invariant/Algorithmic Problem

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The discussion revolves around a mathematical problem involving 25 large empty boxes, which are filled with medium and small boxes, ultimately totaling 291 boxes. Participants explore how to define variables for empty and total boxes, leading to the formulation of equations to calculate the number of empty boxes. The key invariant discussed is the relationship between total boxes and empty boxes, expressed as t - e = L + M, where L and M represent filled large and medium boxes, respectively. Through trial and error, the solution reveals that there are 253 empty boxes in total. The conversation emphasizes understanding the invariant and the relationships between the variables to solve the problem effectively.
  • #51
SpunkyDonutz said:
253 empty boxes

L = 18
M = 20

Thanks :D

(yes, 253 is correct, but …)

wait a moment

L doesn't have to be 18

did you use L = 18 to get that?

if so, you're missing the point
 
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  • #52
tiny-tim said:
L doesn't have to be 18

Yeah, I know it's just one of the many possibilities I know of.

tiny-tim said:
did you use L = 18 to get that?

if so, you're missing the point

I did 298 - 25 - 38 to get it.
 
  • #53
SpunkyDonutz said:
I did 298 - 25 - 38 to get it.

298? 25? :confused:
 
  • #54
tiny-tim said:
298? 25? :confused:

Argh, I'm not thinking straight, bouncing between two assignments.

I meant 291 - 38.
 
  • #55
SpunkyDonutz said:
291 - 38.

ah, that's ok then :smile:

yes, t - e = L + M, and L + M = (291 - 25)/7
 
  • #56
tiny-tim said:
ah, that's ok then :smile:

yes, t - e = L + M, and L + M = (291 - 25)/7

Thanks a lot for the help, I really appreciate it! :smile:
 
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