Is there any good puzzle games on Steam right now?

x+y = x+y

it’s not rocket science—it’s basic numerical diplomacy. 5 plus 1 and 4 plus 2 are structurally identical operations involving distinct pairs that sum to the same total, whether you like it or not. We're not here to babysit digits; we're here to recognize equivalence when it smacks us in the face. You don't need to "solve" both sides—just open your eyes, acknowledge the parallel construction, and move on with your life.

It has an equals sign, therefore both sides are equivalent.

but what if they aren't

Then you have given me an impossible task.

I did no work all through highschool and had a 0 in every class but would pass at the end of the year because I would do well on the eoy tests. I did the same thing with my SATs and got into a good college. I then did the same thing in college.
I will not do busywork

Is that a 1 or an I?
4+2=5+1 or 4+2=5+I?

hold up hands

5 fingers in one hand and 1 on the other

5 + 1

turn hand sideways

thumb is next to finger on the other hand

2 + 4

What's the issue?

4 is 1 lower than 5
2 is 1 higher than 1
The differences cancel out and both sides are the same.

based. the purpose of schools isn't to teach but to do selection.

You didn't even get it right.
You have different values for x and y
That's solving it, which it literally tells you not to do.

4 + 2 = 5 + 1
4 + 2 = 6
move 1 from the 2 to the 4 and you get
5 + 1 = 5 + 1

I only solved one side of the equation. Get fucked.

WITHOUT solving both sides of the equation

First grade my ass

this, you can get the same numbers on both sides by adding and subtracting from those numbers, then since its the same numbers on both sides they must be equal, and this does not require solving either side

and now you're an unemployed retard on Anon Babble, amazing

I hated questions like this because they were often pedantic and looking for specific, teacher-implied answers rather than actual critical thinking.

In any case, since we have to avoid the most obvious reason, I'd just point to the next most obvious. The numbers on the left are a digit off from those on the right, 4 is one less than 5 and 2 is one more than 1. This is proof in pattern, without needing to solve their totals. For example, that rule can prove it even if the numbers were too large to solve on a glance, like 888888888 + 55554 = 888888887 + 55555 + X. You can use that pattern to know X must be 0 without solving the equation.

which is solving, lol

4+2 = 5 +1
It does not tell us we can't shuffle stuff around it only says we can't solve it.

We will simply transform left part by subtracting 1 from 2 and adding to 4
5+1 = 5 +1

Note that it is still not solved.

P.S. I googled the solution after I wrote this and I was correct

if the apples weigh the same, then you can weigh each side and find out they weigh the same. wouldnt know if it was 10 apples or 10,000 apples, but youd still know they were equal amounts on each side. it would be the only thing youd learn, actually.

kek

Aren't all the solutions solving both sides?

go back to faggot

Non of you fags had to do proofs in college and it shows

5 is 1 higher than 4 and you have a one in that 2 so you put that 1 (from the 2) into the 4 and then you have 5+1=5+1

that's still solving each side of the equation

If you haven't play Antichamber.

5 + 1 = 4 + 1 + 1 = 4 + 2

4+2 = 5+1

break 2 into ones

4+1+1 = 5+1

add one of the ones to the 4

5+1 = 5+1

both sides now equal without needing to solve

Asking mathematical proofs for 1st grade math

What the fuck kind of advanced AP class is that? It takes an entire book to prove 1+1 = 2.

You're solving it. You're supposed to answer without solving it.

that game makes me nauseous with all the colors

I got through pre calculus in HS which was our 2nd hardest college math and proofs was always a struggle for me. I could solve math left and right but the structure of proofs was rigid and felt like it stripped away the parts your brain handles intuitively. Only failed one test and it was the proofs segment

it weighs both 1.2 kgs on each side. how many apples is that, on both, or either sides?

I only solved one side, not both sides. The OP says "without solving both sides", not "without solving either side".

oh wait you didnt quote my other better answer nevermind.

you have to do proofs since high school geometry though

I enter 4+2 and 5+1 in a calculator and show you the results are the same. I didn't solve it, the calculator did. Stay mad

based

Sure and guns kill people

4 + 2 = 5 + 1
4 + ( 1 + 1 ) = ( 4 + 1 ) + 1
4 + 1 + 1 = 4 + 1 + 1

I think this question is missing a "if not, explain why".

I'm going to take the dub on this once since nobody has (You)d me trying to prove me wrong, I officially possess at least 1st grader intellect

uhh....

keep subtracting one from both sides, if both sides are 0 then they're equal.

what the fuck are 'mathematical proofs'
isnt that an oxymoron?
if you need a proof for your math and your proof is more math, then why wouldnt you need proof for your proof?

You have to teach it so even the lowest performing 1st grader can understand. Here's pic for that same logic.

cool, ima teach this to my 5yo

A proof is more like a logical argument rather than a solution to an equation. It is used to define and prove mathematical axioms and theorems that many people may take as a basic fact without any thought process (via heuristics).

Minus 4 from both sides and get 2=1+1
Minus 1 from both sides and get 1=1

4+2=5+1 /*x, xeR
4x+2x=5x+1x
6x=6x / *1/6
x=x

ez.

4+2 =6
Increase 5 by one
Decrease 2 by 1
You get a neutral equation which is equivalent to 4+2 without being 4+2. And we know what answer 4+2 got us. So by definition of math's arbitrary axiomatic rules. 5+1 must also equal 6. Since the way in which we arrived at 5+1 neither added an extra number. Nor took away an extra number.

I thought this was a gayer trick than it seemed, because i hate math and its arbitrary rules. But it's actually fairly simple since logic still exists and logic is cool unlike math.

Define equality (=) with the following properties:
- Reflexivity, or that a number is equal to itself. a = a
- Symmetry, or that if a = b then b = a
- Transitivity, or that if a = b and b = c then a = c
- Substitution, or that if a = b then in any expression f(a) we can replace a with b
- Congruence: or that if a = b then a + c = b + c

Define the set of Natural numbers with the following axioms:
- The base element, 0
- The Successor function S(n), which colloquially defines "the next number after n"

Finally define Addition as: a + 0 = a, a + S(b) = S(a + b)

We can now express the original equality in terms of recursive Successor functions, applying the formal definition of Addition:
4 + S(S(0)) = S(4 + S(0)) = S(S(4)) = S(S(S(S(S(S(0))))))
Thus, 4 + 2 = S(S(S(S(S(S(0))))))
Following the same logic, 5 + S(0) = S(5 + 0) = S(5) = S(S(S(S(S(S(0))))))
Thus, 5 + 1 = S(S(S(S(S(S(0))))))

By reflexivity of equality, we have now shown that 4 + 2 = 5 + 1 in terms of recursive Successor function applications.

5=4+1
4=3+1
2=1+1
1+1+1+1 + 1+1 = 1+1+1+1+1 +

Hey, asshole, I got a job

nerd

It's not enough that you can prove math realistically, but also philosophically since not every mathematical theorem can be displayed by gathering physical objects together every single time. I think the first proof every kid grows up learning math is proving the Pythagorean theorem true by using a right triangle and squares like pic.

Just imagine teaching a robot how to do math with it asking why over and over again. You'll have to come up with something like for it to stop asking why.

t.

no