$1484 / (7 / 9) = 19$

Make the equation true by moving one continuous shape or operation in the equation.

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  • 4
    -1 until the directions become more clear on what is expressly allowed. – user1717828 Sep 12 at 19:53
  • 2
    @RohitJose There are multiple distinct answers that fit those rules. – maxathousand Sep 12 at 20:34
  • 3
    Is there a valid solution in this puzzle? – u_ndefined Sep 13 at 11:18
  • 4
    By continuous shape, do you mean a contiguous black shape? Not a region containing multiple separate black shapes? Is it acceptable to change numbers into other numbers by overlaying lines on them? Is it acceptable to break a shape and move only part of it? Is grouping/parentheses considered a single operation (I mean, can you freely move both parentheses around, or must any movement just be one parenthesis?). I've been staring at this for way too long... – Justin Sep 13 at 18:19
  • 4
    I think I have to downvote - the rules keep changing, and even though there has been a series of answers that met the rules at the time, you've changed the rules to make them invalid. This has become a game of "guess what I am thinking" not "find a valid answer". – eedrah Sep 14 at 14:15

14 Answers 14

up vote 5 down vote accepted

In a similar method to Vaelus' answer, take the

empty space above the equation connecting the 8 and the second /, like so: step 1

EDIT: The continuous shape that I've extracted is given by the blue here, which fits the requirements of the original question:

step 2

If you then

rotate this 135 degrees clockwise, you will see that the slash is now vertical and looks like a 1, and the 8 looks like two diagonal zeros step 3

Either

shrink this

or

change the distance of the two pieces from the viewer to simulate zooming. It will look like the following: step 4 Superimpose this back on the remainder to get this: step 5

Which gives us

the modulo operator, and the equation 1441 % (79) = 19

Which is true

  • 2
    Wouldn't this be considered moving two things? – Robert S. Sep 13 at 22:00
  • 1
    Yes, that is moving two things – Rohit Jose Sep 14 at 6:33
  • Despite a mistake in an earlier version of my answer, in the current version, you can see I move only the background, without moving any of the symbols on top of it. In my original conception, moving the background would have left the foreground color, analogously to how moving the foreground color leaves the background color. This would have left the characters on top completely "invisible". However, I opted to go for the more humorous circuit board design, with the other symbols barely perceptible over it. – Vaelus Sep 14 at 9:03
  • I've added another image to show that this meets the requirements of the question, by "moving one continuous shape". It is moving two glyphs, but they are connected by a continuous shape. – eedrah Sep 14 at 14:11
  • 1
    This is the correct answer? – Robert S. Sep 14 at 15:05

If you move the continuous region of background outlined in red to the indicated location: enter image description here The equation becomes true:

enter image description here

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  • 2
    Hahhah, this made me laugh. Very creative – maxathousand Sep 12 at 19:27
  • Wow... that’s unbelievable... I never thought of that – Rohit Jose Sep 12 at 19:43
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    I like the circuit board. Nice touch – Cullub Sep 13 at 13:11
  • I don't get this answer, is the slash supposed to represent a slanted one? – Anthony Pham Sep 13 at 21:47
  • @AnthonyPham Yes, although it's certainly not good style. I don't know what the author was thinking. – Vaelus Sep 13 at 21:49

Maybe

Take the first(or second) slash/division and put over the equal sign(that's what everyone else does).

To get

1484(7/9)≠19

If this is allowed :p

  • 3
    Nooooo! Not that! UGHHH! Do I have to specify this every time I make something like this? – Rohit Jose Sep 12 at 17:33
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    For what it’s worth, I officially approve of this answer haha! – El-Guest Sep 12 at 17:56
  • I think you meant to write second. – Weather Vane Sep 12 at 17:59
  • 2
    "Do I have to specify this every time I make something like this?" Only if you want to ask a community that tries its hardest to bend the rules... I mean think laterally to get an answer. – Alpha Sep 12 at 23:10
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    @Alpha I know... I know... – Rohit Jose Sep 13 at 17:25

Move the $1$ in $1484$ and move it to cross the $1$ in $19$.

$484 / (7 / 9) = x9$

The solution to this equation is $x = 484/7$.


UPDATE: In response to the hint (I'm sure this is still not the answer OP is wanting, however, it fits the rules just fine), the same trick can be done by moving either of the division signs.

$1484 (7 / 9) = x9$; Solution: $x = 10388/81$
or
$1484 / (79) = x9$; Solution: $x = 1484/711$

  • 1
    This is interesting, but not right because you haven’t defined the x, so you don’t know if it’s correct – Rohit Jose Sep 13 at 15:03
  • @RohitJose Did I misinterpret any of the rules? There seems to be many valid answers... – maxathousand Sep 13 at 15:04
  • @RohitJose An equation is a statement that the values of two mathematical expressions are equal (source). This is, by definition, an equation, just as $a = b$ is an equation. – maxathousand Sep 13 at 16:20
  • 1
    but is it true? – Rohit Jose Sep 13 at 16:47
  • I may be speaking out of my expertise here, but I don't believe it's possible to call an equation that includes an algebraic expression true or false. If you mean "solvable", then yes, there exists a solution for which $484/(7/9) = x9$ is true. All of this really is irrelevant to solving your puzzle, as you've already indicated this is not the answer you have in mind. Would you consider adding a hint to narrow down the possible answers? – maxathousand Sep 13 at 17:01

An alternative solution...

Take the $=$ sign and spin it 90 degrees to make it into a logical OR operator $||$. Thus, the resulting expression is: $1484/(7/9) || 19$ which equates to TRUE since both sides of the || are not equal to $0$.

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  • Welcome to Puzzling.SE! I would imagine that this falls under the "no inequality signs" rule, which is designed to prevent exactly these sorts of sneaky answers. – F1Krazy Sep 12 at 19:15
  • Wow I didn’t think of that! Well done, but as above, no cheaty answers – Rohit Jose Sep 12 at 19:19
  • I don't think this is making an inequality sign. If OP doesn't want someone touching the = he should expressly disallow moving or modifying it. – user1717828 Sep 12 at 19:25
  • 1
    Done. How’s that then? – Rohit Jose Sep 12 at 19:39

I'm sure this isn't what you want either:

Assuming rotation is allowed, move the second division sign over to the equals sign and make it "defined as".

Like:

1484/(79) ≡ 19. Not sure why you'd want to define it this way though...

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  • 1
    Good idea, but not correct – Rohit Jose Sep 12 at 18:25

I think if

The equation was formed like $1484 / (\frac 7{9}) = 19$

We could

Move a copy of $\frac 7{9}$ over the $84$ to make it $14\frac 7{9} / (\frac 7{9}) = 19$

  • That's an interesting idea, but incorrect – Rohit Jose Sep 13 at 19:34

Well, I'm sure this isn't the correct answer; however, if you round up!

14(84/7/9) = 18.6... rounded up = 19.

  • 1
    Good, but no rounding – Rohit Jose Sep 12 at 18:00
  • 1
    If you leave a down-vote, please comment and explain how I can improve my post. – PerpetualJ Sep 12 at 21:00

Take the

First division sign

and use it to

strikethrough the 4, 8, and 7

to get

$1$484(7/$9)$$=19$

Or

$19=19$

SOLUTION #2 Re-read the title.

The 'thing' i'm putting in the equation is

08, at the end.

Which is

$1484/(7/9)$ $=$ $1908$

Math:

$1484/(7/9)$ --> $(1484*9)/7$ --> $1908$

  • The ROT13(svefg qvivfvba fvta) is not that long! – Wais Kamal Sep 12 at 19:05
  • Good idea, but what about the dots? Also, yes, as Wais Kamal said, it’s not THAT long – Rohit Jose Sep 12 at 19:09
  • Oh yea. Right. Back to the drawing board with more CREATIVE solutions – Alto Sep 12 at 19:11
  • I see where you're going with the second solution, but "08" would not be considered a continuous shape since the two numbers are separated. – Robert S. Sep 12 at 19:50
  • Seriously? Sigh. – Alto Sep 12 at 19:55

I'm pretty sure this is not what you want either, but

if you take the bottom line of the equal sign and tilt it upward, you make an awkward greater than sign and $1484/(7/9)>19$ is true.

  • xhienne tried this already, but good try – Rohit Jose Sep 12 at 19:17
  • @RohitJose SteveV was first to propose an inequality. But this one is different. – xhienne Sep 12 at 20:21
  • No equalities as well – Rohit Jose Sep 12 at 20:51

A similar idea as others who have fiddled with the equal sign:

move the second / over the equal sign in order to make a sign

This yields: $1484/(79) ≤ 19$

(which is correct since 1484 / 79 ~= 18.78)

  • 1
    This would require two moves, so I don't think it qualifies. – Robert S. Sep 12 at 18:47
  • No @RobertS, the equal sign doesn't change despite what the font is displaying. – xhienne Sep 12 at 18:49
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    Also, the problem is to make a true equation – Vaelus Sep 12 at 18:53
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    @RohitJose That seems unfair then. Now this puzzle has devolved into a "guess what I'm thinking" game. – maxathousand Sep 12 at 19:23
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    @maxathousand Ok, let me rephrase, as seen now in the question, no messing with the = sign – Rohit Jose Sep 12 at 19:41

If we could

take the slanty bit off the top of the first 4

We are left with

1 + 84 / (7/9) = 19

and we can

place a single straight line somewhere

to make it all work out.

But

1 + 84/(7/9) = 109

and I can't find a way to

turn 19 into 109 by adding a single straight line

(or any other way to proceed down this line of thinking)

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  • You are not on the right track, but good try – Rohit Jose Sep 13 at 19:33
  • You can even get to the same place by removing the first 4 entirely. The left hand side 1 84/(7/9) could arguably be considered implicit multiplication by 1 or addition of 1 like a strange mixed fraction, to get 108 or 109. I can't figure out how to use a 4 on the right hand side either though. – Justin Sep 13 at 19:35

If you

lasso a region containing the two 1s and move them both down a bit, you end up with

$1^{484/(7/9)} = 1^9$

Each side just simplifies to get

$1 = 1$

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  • 2
    Good answer, but that moves 2 ones. Welcome to Puzzling.SE! Also, the hint says "don't move a digit" so, yeah. – Alto Sep 13 at 23:30
  • It moves 2 ones, but by the same amount, and you could easily define a single region containing only them. Seems just as legitimate as the accepted answer to me. – Justin Sep 15 at 18:28

You can simply move the

second division sign to connect the tail of the 9 to the bottom of the circle of the 9, making the 9 into an 8. As a result, the equation is now $$1484 / (78) = 19$$ As long as we use the computer science / operator, namely floored division, the equation is true.

  • Good try, but I was meaning that to be the division operator, the floor operator is // – Rohit Jose Sep 14 at 6:35

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