1. Consider the "equation" $6145 - 1 = 6143$. Can you move two digits so as to create a valid equality?
  2. The equation $-127=-127$ is, of course, true. Suppose you were told again to move two digits as to leave a valid equation. Please note that you have to move two digits on the same side of this equation.


Moving means that you can change the position of any two digits independently, so that they still are a number/constant!


The moving doesn't require swapping of digits in both.

It is a part of mathematical puzzles asked in the puzzling contest at my college(coordinated by me).

  • 1
    $\begingroup$ Can you clarify what you mean by "move two digits"? Exchange their positions? Move them to any position? $\endgroup$ – frodoskywalker Feb 22 '16 at 18:36
  • $\begingroup$ Ok, I am adding a hint. $\endgroup$ – ABcDexter Feb 22 '16 at 18:37
  • 6
    $\begingroup$ That still doesn't quite answer the question - what exactly is permitted by "moving" digits? $\endgroup$ – DylanSp Feb 22 '16 at 18:44
  • $\begingroup$ Anything, which keeps the mathematical meaning intact. $\endgroup$ – ABcDexter Feb 22 '16 at 18:57

First one:

$614-1^{54}=613$ or $615-1^{43}=614$

Second one:



Lateral thinking says I can move these two digits in this way:

By using the $1$ as a line instead of a number,
1. $614 − 5 \ne 6143$
2. $-127 \ne 72$

  • $\begingroup$ Not sure why the downvote. The "lateral-thinking" tag is applied, and I followed the instructions of moving digits. $\endgroup$ – Ian MacDonald Feb 23 '16 at 15:09
  • $\begingroup$ I upvoted your answer, as it used to be a valid escape route to just make that tricky change into inequality... $\endgroup$ – ABcDexter Feb 24 '16 at 19:22

The second one is fairly easy (makes me think I might not quite understand where you can "move" a digit):

$2-17 = 2-17$ OR $1-27 = 1-27$ OR $-217 = -217$ or pretty much anything else like that.

Here's a solution to the first one that takes advantage of the vagueness of the instructions. I'm not sure if it's "legal" though.

Remove the $1$ from the $6145$ and put it sideways, turning it into a subtraction sign. Then move the $1$ from $6143$ over to the other side. You'll end up getting $645-1-1=643$.

  • $\begingroup$ Good try, but please look at the updated question :-) $\endgroup$ – ABcDexter Feb 22 '16 at 18:53

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