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Upon reaching the door to the office, instead of a normal keypad, you are presented with a strange grid. Tacked to the wall there is a punch-card with five columns, each column containing the numbers from zero to nine. At the top of each column there is also a blank dot, as well as a dot with a decimal point at its center.

You can only assume that the answer to the strange grid must be entered on the punchcard, which in turn must be inserted in a credit card sized slot in the wall.

Seeing the strange slashes and the mathematical symbols, you begin to panic. Math wasn't your forte in school, and now, your life may depend on your completion of this problem.

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What is the password that this grid holds in its solution?

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    $\begingroup$ Reminds me a bit of ><>... (interpreting / and \ as mirrors gives us the sequence 9 x 3 x^2 + 3 x 1/6 + 22 sqrt $ euro) $\endgroup$ Commented Jan 31, 2016 at 4:20
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    $\begingroup$ Also, how can the each column contain the ten digits 0-9 if there are only five rows in each column? A picture of the punch card would be helpful. $\endgroup$ Commented Jan 31, 2016 at 4:25
  • $\begingroup$ The punch-card is 5 rows wide, each row containing the digits 1-9 etc.. The purpose of this is to show you the length of the finishing sequence. $\endgroup$ Commented Jan 31, 2016 at 14:13
  • $\begingroup$ @2012rcampion You are distressingly close... $\endgroup$ Commented Jan 31, 2016 at 17:38
  • $\begingroup$ Do you mean the punch card is five columns wide? (and that the dots are at the top of each column, since rows don't have tops) $\endgroup$ Commented Jan 31, 2016 at 19:07

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The grid reminds me a bit of ><>, an esoteric programming language where the program pointer moves around on a two-dimensional grid of characters.

In ><>, the two slashes / and \ are reflectors. Think of the program flow 'bouncing' off of them like hitting a wall. Assuming the same initial condition as ><> (starting in the upper-left corner headed right), and that none of the other characters modify the program flow, we get a flow like:

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The sequence of 'instructions' we pass through is:

9 x 3 x^2 + 3 x 1/6 + 22 sqrt $ euro

I assume that the different color of the 9 is probably just to indicate that it is the starting point, and that the > indicates that the flow exits to the right.

Interpreting x as times, the first ten characters look like a mathematical expression written as a series of key to enter into a calculator:

$$ 9 \xrightarrow{\times 3} 27 \xrightarrow{x^2} 729 \xrightarrow{+3} 732 \xrightarrow{\times\frac{1}{6}} 122 \xrightarrow{+22} 144 \xrightarrow{\sqrt{x}} 12 $$

The two currency symbols, however, are still a mystery. Presumably they indicate some sort of exchange rate conversion. However, exchange rates are changing constantly and we lack a fixed time to determine a fixed exchange rate. Also, we need (according to Hanko) a five-digit number. Converting from USD to EUR is not a big change, so the integer part will remain two digits; and since both currencies are divided into exactly 100 subunits, that leaves us only two further decimal places, four total out of five.

Personally, If I were you, and believed that:

your life may depend on your completion of this problem

I'd probably just stop working there.

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  • $\begingroup$ I'm not so sure about the five digit number bit. They did say the length was five, but there are also the symbols. $\endgroup$ Commented Jan 31, 2016 at 23:09
  • $\begingroup$ @Will But the columns only have the digits 0-9. $\endgroup$ Commented Jan 31, 2016 at 23:10
  • $\begingroup$ The last sentence of the first paragraph says otherwise. $\endgroup$ Commented Jan 31, 2016 at 23:11
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    $\begingroup$ @Will Ah, my mistake! I assumed that the decimal points were between columns. I think we need a picture... $\endgroup$ Commented Jan 31, 2016 at 23:12
  • $\begingroup$ Good answer! I did draw inspiration from ><>. As for the $ to euro, I agree completely that I would leave it as is. Next time, I will make my question more clear. Sorry for the discrepancies. $\endgroup$ Commented Feb 1, 2016 at 0:20

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