5
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A mad puzzle enthusiast locks you inside a room with only one door. Next to the door is a standard numeric keypad. There is no way to escape except through the door. You find a piece of paper next to the keypad:

$181 \Rightarrow E \unicode{12288} 3$

$3 \unicode{12288} -E \Rightarrow \unicode{xFF1F}$

You turn the piece of paper over and see two more scribbles.

$E = 1$

The answer is not in sight.

What do you type in the keyboard to escape, and how did you figure it out?

Hint 1:

You notice that the puzzle enthusiast had one more equation but erased it. Following the indentations on the paper, you find out that it said: $3 \unicode{x005F} 1 \Rightarrow 1A3$

Big Hint 2:

The numbers on the keypad are all in seven-segment display. You wonder if that means anything...

Since this is my first puzzle, any feedback would be appreciated.

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  • 1
    $\begingroup$ ...I'm not noticing any suspicious blank spaces. Am I also mad? $\endgroup$ – Bailey M Aug 5 '15 at 15:39
  • $\begingroup$ I elaborated on the location of the spaces in hint 1. $\endgroup$ – heypeople Aug 5 '15 at 15:41
  • 2
    $\begingroup$ Would using an underscore for the blank spaces work, or would it interfere with the solution? $\endgroup$ – LogicianWithAHat Aug 5 '15 at 15:45
  • $\begingroup$ Refer to my third hint that I just added. $\endgroup$ – heypeople Aug 5 '15 at 15:52
  • $\begingroup$ For clarity, I made the white spaces more prominent. $\endgroup$ – heypeople Aug 5 '15 at 16:43
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That big hint is a rather big hint.

Punch in

$1801$

The first one:

$181 \Rightarrow E \space 3$
Here, the 7-segment display is inverted for each number.

The second one has four entities on the left-hand side, so there will be four on the right-hand side.

$3$ inverted gives $1$.
$\space$ inverted gives $8$.
$-$ inverted gives $0$.
$E$ inverted gives $1$.


Old answer left in for posterity.

Punch in:

12

When you consider that

the spaces could stand for something, we can make them stand for $+17$.

This gives us:

$181 \Rightarrow E+173$ and $3+17-E \Rightarrow ?$

From the first, we see that

$E = 8$

which we can now plug in and solve as:

$3+17-8 = 12$

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  • $\begingroup$ Good try but unfortunately not the answer. I removed the math and pattern tags because I think they are misleading. The answer is less complicated and does not use conventional math. Also, your answer does not explain the third hint. $\endgroup$ – heypeople Aug 5 '15 at 17:46
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    $\begingroup$ @heypeople that's because I couldn't decide if the underscore was intentional, or if it was also supposed to be a space like the others. $\endgroup$ – Ian MacDonald Aug 5 '15 at 17:57
  • $\begingroup$ The underscore is intentional, it is separate from the spaces. $\endgroup$ – heypeople Aug 5 '15 at 18:08
  • $\begingroup$ I just added the final clues so it should be clearer now. $\endgroup$ – heypeople Aug 5 '15 at 18:14
  • $\begingroup$ Yes, I do agree it is a rather big hint. Sorry puzzling community, I didn't have enough faith in you guys. $\endgroup$ – heypeople Aug 7 '15 at 17:31

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