Empty Boxes Invariant/Algorithmic Problem

[SpunkyDonutz]

that's no way to pass an exam

ii] what is the formula for the total number of all boxes (in terms of l and m), that has to be 291 ?​

(7*25) + 25 = 200

 

[SpunkyDonutz]

Which leaves enough space for 13 medium boxes to be filled with small boxes.

 

[tiny-tim]

ii] what is the formula for the total number of all boxes (in terms of L and M), that has to be 291 ?​

(7*25) + 25 = 200

there's no L or M in that

 

[SpunkyDonutz]

there's no l or m in that

(7l) + 25

 

[tiny-tim]

(7l) + 25

so far, so good

what about M?​

 

[SpunkyDonutz]

so far, so good

what about m?​

7l + 7m + 25

 

[tiny-tim]

7l + 7m + 25

Woohoo!​

ok, if 7L + 7M + 25 = 291, what can you say about L and M ?

 

[SpunkyDonutz]

Woohoo!​

ok, if 7L + 7M + 25 = 291, what can you say about L and M ?

7L + 7M + 25 = 291
= {-25 from each side}
7L + 7M = 266
= {let L be 18}
(7*18) + 7M = 266
= {Simplify}
126 + 7M = 266
= {-126 from each side}
7M = 140
= {140 / 7 = M}
M = 20

L = 18
M = 20

 

[tiny-tim]

{let L be 18}

why?

 

[SpunkyDonutz]

why?

It works, I have no clue on how to solve two variable equations.
Couldn't find anything helpful on the net either.

 

[tiny-tim]

remember: you know t = 7L + 7M + 25

and you know e = 6L + 6M + 25

so what you can you say about the relation between t and e ?​

 

[SpunkyDonutz]

remember: you know t = 7L + 7M + 25

and you know e = 6L + 6M + 25

so what you can you say about the relation between t and e ?​

t - e is the invariant.

 

[tiny-tim]

t - e is the invariant.

hmm … i need to remind myself of the original question …

1. Introduce the variables e and t for the number of empty and the number of
total boxes, respectively.
2. Identify the information that is given about the initial and final values of e and
t.
3. Model the process of putting seven boxes inside a box as an assignment to e
and t.
4. Calculate an invariant of the assignment.
5. Combine the previous steps to deduce the final value of e

i honestly don't know what an "invariant" is in this context , so i can't say whether you're right or not

but t - e is certainly very important!

can you solve t - e ? ​

 

[SpunkyDonutz]

i honestly don't know what an "invariant" is in this context , so i can't say whether you're right or not

An expression that doesn't change.

but t - e is certainly very important!

can you solve t - e ? ​

The calculation would be:
(6(L + M) + 25) - (7(L + M) + 25)

But I don't know what the outcome would be.

 

[tiny-tim]

remember: you know t = 7L + 7M + 25

and you know e = 6L + 6M + 25

so what is t - e ?​

 

[SpunkyDonutz]

remember: You know t = 7l + 7m + 25

and you know e = 6l + 6m + 25

so what is t - e ?​

m + l

 

[tiny-tim]

m + l

ok, and you know 7M + 7L + 25 = 291

sooo … ?​

 

[SpunkyDonutz]

ok, and you know 7m + 7l + 25 = 291

sooo … ?​

l + m = 38?

 

[tiny-tim]

yes of course

and you should be able to solve the problem now​

 

[SpunkyDonutz]

253 empty boxes

L = 18
M = 20

Thanks :D

 

[tiny-tim]

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

 

[SpunkyDonutz]

L doesn't have to be 18

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

did you use L = 18 to get that?

if so, you're missing the point

I did 298 - 25 - 38 to get it.

 

[tiny-tim]

I did 298 - 25 - 38 to get it.

298? 25?

 

[SpunkyDonutz]

298? 25?

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

I meant 291 - 38.

 

[tiny-tim]

291 - 38.

ah, that's ok then

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

 

[SpunkyDonutz]

ah, that's ok then

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

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