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So, I need your help.

I got home after a long day and found a calculator roughly taped to my door. However, there was something much more disturbing attached to that calculator. It was some kind of black device with a blinking red 12 on it. There was also a note which I read.

Hello... In order to live, you must defuse the bomb by making the calculator show the number 212. However, you only have 12 key presses to do it, including the = key at the end. Don't try to enter your house through a window or opening a door, or any other way, or the bomb will go off. Don't call the police or anyone to help, either. This message contains no hints, so it's a waste of time looking for them. In addition, this calculator is modified so that you can't press a number when there's a number and no operation in (for example, you can't press the 6 key if the calculator shows 89 with no equation.)

Easy. I was about to hit 212 Enter when I noticed, the 2 and 1 keys were broken. So were so many keys, that, it's easier to list the keys that weren't broken.

Keys remaining: $0, 4, 7,+, -, x^2, 10^x, =$

Note: The $x^2$ and $10^x$ keys give their result immediately, without requiring another key press.

The calculator currently displays the number $5$.

One last thing: You must hit the = sign at the end.

Good luck. I definitely hope you have it, because I need some right now.

Also, the tag says no computers, but feel free to pull out an actual calculator and give it a go. Just no computer programs.

If you have any questions on how certain buttons work, feel free to ask me in comments.

CLARIFICATION: The calculator has no memory function, so you can't do equations 'on the side' like squaring a number separately, then adding that number to the main total.

Extra Credit: Can you do it without the + key?

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  • $\begingroup$ No parentheses? $\endgroup$
    – PotatoLatte
    Commented Sep 23, 2018 at 1:57
  • $\begingroup$ No parentheses. $\endgroup$
    – Excited Raichu
    Commented Sep 23, 2018 at 1:58
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    $\begingroup$ "Don't call the police or anyone to help, either"... heh heh heh $\endgroup$
    – PotatoLatte
    Commented Sep 23, 2018 at 1:59
  • $\begingroup$ I don't think I understand how this calculator is supposed to work; it certainly isn't the same as any real calculator I've ever used. Is the idea that when you hit the "squared" button it first of all behaves as if you have pressed the = key, and then squares the result? $\endgroup$
    – Gareth McCaughan ♦
    Commented Sep 23, 2018 at 2:02
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    $\begingroup$ 1. 5 is already typed in. You cannot add numbers to it right now (because you can't press a number in when there's an already existing number in with no equation.) 2. $10^x$ computes 10 to the power of whatever number is in the display at that moment, as does $x^2$ (except it squares the current number). 3. The calculator is like that to make it harder :^) $\endgroup$
    – Excited Raichu
    Commented Sep 23, 2018 at 2:07

3 Answers 3

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[OP has clarified the somewhat unorthodox behaviour of the calculator; my earlier answer, preserved below, no longer applies but we can do something else instead.]

Do this:

+ 4 + 7 sq - 4 4 =

That will

add 4+7 to our initial 5, getting 16; square it, getting 256; subtract 44, getting 212.

We have used

9 keypresses in total.

If we need to use the full 12 keypresses, we can

follow up with + 0 = which of course changes nothing.

Old answer, applicable to real calculators

I think I can do it in 11 key presses:

sq - 4 - 7 = sq + 4 sq =

So

after squaring the calculator shows 25; we subtract 4 and 7 to get 14; we square to get 196; we add 4^2=16 to get 212.

If we need to use exactly 12 key presses we can

press = after subtracting 4.

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  • $\begingroup$ 1. It is stated that you need to hit the = sign at the end. $\endgroup$
    – Excited Raichu
    Commented Sep 23, 2018 at 1:56
  • $\begingroup$ I did. Have I misunderstood something? $\endgroup$
    – Gareth McCaughan ♦
    Commented Sep 23, 2018 at 1:57
  • $\begingroup$ and 2. It wouldn't be possible to add 4^2 at the end, because the ^2 would square the entire thing, getting a very large number. $\endgroup$
    – Excited Raichu
    Commented Sep 23, 2018 at 1:57
  • $\begingroup$ Really? Not on any calculator I've used. $\endgroup$
    – Gareth McCaughan ♦
    Commented Sep 23, 2018 at 1:58
  • $\begingroup$ Huh. I'll reword the question to include that. $\endgroup$
    – Excited Raichu
    Commented Sep 23, 2018 at 1:58
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Going off of Gareth's answer a bit, for extra credit (no '+' key), we can try

- 7 sq sq sq - 4 4 =

Which works (I think) because

$5-7=-2$
$(((-2)^2)^2)^2=256$
$256-44=212$

and uses

8 keypresses in total.

For exactly 12 keypresses,

We can follow with - 0 0 = which changes nothing.

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Okay, here goes.

We start with $5$,

$+70+70+77=$ somehow has 10 key presses!!!

And,

$5+70+70+77=212$

I did it.

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  • 4
    $\begingroup$ That equals 222 $\endgroup$
    – PotatoLatte
    Commented Sep 23, 2018 at 2:09

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