49

I display to you a set of 5 equations that cannot be solved*.

I want you to find the solution:

B + C = 1
B + C + F + G = 4
A + B + C = 7
A + B + C + D + G = 3
A + B + E + D + G = 2

Time’s ticking, don't wait around!

What is the solution to the above equations?

*cannot be solved as in, the equations do not have a unique solution.

Beastly Gerbil
  • 58,036
  • 8
  • 166
  • 314
  • 4
    If they cannot be solved, why do you want us to find the solutions? :P . – Anonymous Dec 30 '20 at 15:27
  • 1
    @Anonymous well... they cannot be solved, but I can confirm there is a solution ;) – Beastly Gerbil Dec 30 '20 at 15:32
  • Can be solved by lateral thinking! – DrD Dec 30 '20 at 15:52
  • @DrD I feel like that tag would give it away too much – Beastly Gerbil Dec 30 '20 at 15:53
  • Absolutey @BeastlyGerbil. With that tag even I would have solved it!! May be not :) – DrD Dec 30 '20 at 15:54
  • 2
    The answer given by user39583 is definitely nicer but as it stands the system of equations can be solved and has more than one solution. Say A=6, B=2, C=-1, D=-6, E=-2, F=1 and G=2 is a solution if I didn't screw up my algebra. – quarague Dec 31 '20 at 11:18
  • 2
    @quarague very true, I have a feeling even if I wrote out the ‘equations’ for every number that can be made there would still technically be a real solution. I’ll just claim that the fact there are multiple solutions means there’s not an ‘exact’ solution :) – Beastly Gerbil Dec 31 '20 at 11:46
  • Well there are 7 unknowns and 9 (even 10 if you include 0) equations, so I would expect that there is no solution for all equations. I'm just not sure whether that would make a better puzzle. – quarague Dec 31 '20 at 12:59
  • @quarague interesting... I could probably add more to make it actually unsolvable, but for the sake of the puzzle I think it looks better with 5 so I'll leave it as is – Beastly Gerbil Dec 31 '20 at 13:35
  • BeastlyGerbil: the numerical solutions are "exact", they're just not "unique". I'd phrase this instead: "These equations are not intended to be solved numerically. What do they mean instead?" – smci Jan 01 '21 at 12:39
  • 2
    @smci unique is a much better word there I agree. The question is supposed to be quite vague on purpose, but I will change to ‘these equations don’t have a unique solution'. Saying they aren’t supposed to be solved numerically gives too much away – Beastly Gerbil Jan 01 '21 at 13:56
  • BeastlyGerbil: I was strongly recommending you edit the title, not just a tiny footnote at bottom of question body. Because this question is being broadcast as a HNQ, so people will only see the title and come here, and since the "unsolvable" title is incorrect, might wrongly think it was clickbait or spam. – smci Jan 02 '21 at 02:15
  • 1
    @smci I knew what I was doing with the title, and yes to some degree it is clickbait, that’s what a lot of puzzles do. I’ve defined what I mean by unsolvable in the question however, so actually the title is correct as per the question. No one will see this as spam, and most people from HNQ know what to expect when clicking on a puzzle. I see no need to change the title, it’s a nice introduction which will draw people in – Beastly Gerbil Jan 02 '21 at 02:35
  • BeastlyGerbil: then it is clickbait, and knowingly posting misleading clickbait on HNQ is something many people would object to. It's the only thing that prevents us descending into Yahoo Answers, where most of us had to flee the site circa 2012 after it was overrun with people posting "Impossible question" or "Noone can solve this" on a set of linear equations. Please let's keep titles reasonably accurate. – smci Jan 02 '21 at 02:42
  • 2
    @smci I don’t see how the title is misleading. If anything it is more truthful than anything. I have stated that the equations aren’t solvable, said what I mean by solvable, and it is true. There is a solution, but not in the traditional sense. Clickbait is when you title it something completely false or unrelated. This title is both related and true. It is definitely more than ‘reasonably accurate’, and I haven’t seen anyone else have any issues, so will keep it as is. It is also nearly no longer on HNQ anyways if that’s the issue – Beastly Gerbil Jan 02 '21 at 02:53
  • BeastlyGerbil: I disagree, and redefining the word "solvable" inside the question body doesn't fix the title, but anyway. Here's another decent non-spoiler title: "A set of equations without a unique solution... or is it?" – smci Jan 02 '21 at 02:57
  • 2
    @smci I stand by the title being correct. The equations do not have a unique solution, the puzzle does. The equations are unsolvable, the puzzle is not. If anyone has a problem with me saying the equations are unsolvable, I have clarified in the question what I mean. The title suits the question perfectly and is also perfectly acceptable – Beastly Gerbil Jan 02 '21 at 03:01

3 Answers3

52

All the hints point us towards

Seven-segment display. The letters correspond to the segments needed to display each of the numbers.

enter image description here

(Image from the wikipedia page)

Beastly Gerbil
  • 58,036
  • 8
  • 166
  • 314
user39583
  • 8,433
  • 36
  • 42
  • Correct! Good spot :) And I probably overdid it slightly with the hints, but good spot seeing the hints too! – Beastly Gerbil Dec 30 '20 at 15:55
  • @BeastlyGerbil - You should accept this answer as correct. – Vilx- Jan 01 '21 at 00:14
  • 2
    @Vilx- don’t worry I will! I usually leave answers a couple of days before accepting that’s all, but this answer will definitely get the check! – Beastly Gerbil Jan 01 '21 at 00:21
  • @BeastlyGerbil - I don't see the point (especially since you can always change the checkmark if you feel like it), but OK. Fair enough. :) – Vilx- Jan 01 '21 at 00:54
  • 2
    @Vilx- I could be wrong, but puzzles seem to perform better when you don’t accept straight away, and think it affects HNQs too. I make sure to always accept for all my puzzles though :) – Beastly Gerbil Jan 01 '21 at 00:55
  • hell it's like sherlock holmes or something in here. niiiiiiiiiice – BCLC Jan 01 '21 at 19:54
7

This question is really weird and has some weird ambiguities: I'm not sure if I did it right, so please critique my logic! I also don't know how to make the whole thing a spoiler so they are kind of haphazardly placed.

We know that

  1. B + C = 1
  2. B + C + F + G = 4
  3. A + B + C = 7
  4. A + B + C + D + G = 3
  5. A + B + E + D + G = 2

From 1 and 3 we know that

A = 6

From 1 and 2 we know that

F + G = 3

so

G = F - 3

From 3 and 4 we know that

D + G = -4

so

D = -4 - G

so substituting the above equation for G we get

D = F - 3 - 4

so

D = F- 7

and

F = 7 + D

We can substitute the above into equation 2 and 4 to get

B + C + (7 + D) + (3 - G) = 4

so

D = -7

and

A + B + C + (-7) + G = 3

so

G = 3

and substituting this back into equation 2 gives us

F = 0

This is where things get weird:

We know from equations 4 and 5 that

C - E = 1

and using that in equation 1 we find that

C = -B + 1

therefore

B = -E

This means that we can use literally any value for B, and as long as C and E follow the above conventions, all the equations will still be true.

a43nigam
  • 79
  • 1
  • 1
    There's a mistake where you substitute your expression for G; you should substitute (F - 3) so that way D = -4 - G = -4 - (F - 3) = -4 - F + 3 = -1 - F, not F - 7 – bobble Dec 31 '20 at 17:22
  • Interesting, the maths is slightly off at the start, but I imagine the result will still be the same. Quite happy in that case as I didn't want there to be an actual 'solution' rather the solution be the other answer, so quite happy its worked out this way :) +1 for trying to find this answer though! – Beastly Gerbil Dec 31 '20 at 17:44
1

I don't know if there's more than one solution, but my calculations led to:

A = 6
B = 0
C = 1
D = -4
E = 0
F = 3
G = 0

knightofiam
  • 119
  • 2