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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.

enter image description here

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) $\endgroup$ – 2012rcampion Jan 31 '16 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. $\endgroup$ – 2012rcampion Jan 31 '16 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. $\endgroup$ – Quiquȅ Jan 31 '16 at 14:13
  • $\begingroup$ @2012rcampion You are distressingly close... $\endgroup$ – Quiquȅ Jan 31 '16 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) $\endgroup$ – Jack M Jan 31 '16 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:

enter image description here

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. $\endgroup$ – Will Jan 31 '16 at 23:09
  • $\begingroup$ @Will But the columns only have the digits 0-9. $\endgroup$ – 2012rcampion Jan 31 '16 at 23:10
  • $\begingroup$ The last sentence of the first paragraph says otherwise. $\endgroup$ – Will Jan 31 '16 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... $\endgroup$ – 2012rcampion Jan 31 '16 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. $\endgroup$ – Quiquȅ Feb 1 '16 at 0:20

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