# Why would five hundred and five be same as one?

Grandpa was in his crazy math mood again.

"using rot13 and your math knowledge prove to me that

505 = 1"

He said.

Really? Can you?

HINT

Think Trigonometry

• Don't have an answer, but I'll note 2 findings given the hint: 1) 505 is the hypotenuse of a triangle with integer length sides. 2) Rot13-ing the Roman Numerals for the number 105 produces a trigonometric term. Maybe one of these is on the right path and will help someone. – TwoBitOperation Mar 20 at 14:40
• @TwoBitOperation for anyone possibly going with route 1: The possible sides of a triangle that work are (100, 495) (217, 456) (303, 404) (336, 377) – akozi Mar 20 at 16:28

Here's one possible solution:

1. $$505 = 1$$ : Given
2. $$DV = 1$$ : By Romanizing left
3. $$V = 1/D$$
4. $$CV = C/D$$ : Multiply through by 100
5. $$(PI)= C/D$$ : By Rot(13)ing left
6. $$Dπ = C$$

By the circumference formula for a circle (C= πD),the left and right are equivalent

Q.E.D.

• Wow. If that's the intended solution I'll be quite surprised. Regardless, that's an amazingly convoluted way to answer this, and I love it. :) – Rubio Mar 20 at 20:51
• I'm... just as surprised as everyone else here. – TwoBitOperation Mar 20 at 21:44
• @DEEM What does this have to do with trigonometry? – noedne Mar 20 at 21:53
• wouldn't step 5 require you to to do both sides, yielding P/Q? – corsiKa Mar 21 at 0:49
• Step 2 to 3 doesn't make sense, as Roman numerals are additive, not multiplicative. – Herb Wolfe Mar 21 at 3:19

Reasoning

In Roman numerals 505 is DV. If we use rot13 on these two characters, we get QI.
Qi is the circulating life force whose existence and properties are the basis of much Chinese philosophy and medicine. It allows us to say that we are one with the universe. In this way, 505=1

• Lot different than my answer – DEEM Mar 19 at 13:10
• @DEEM Can you tell us a way in which your answer differs from this answer? – Tanner Swett Mar 19 at 18:48
• So there is the rot13 part and there is the math part. Both are needed for my answer – DEEM Mar 20 at 1:36

By using

hexomino's idea of ROT13 on Roman numerals

we can obtain

$$\text{ROT13}(505)=\text{ROT13}(V^4-V^3+V)=I^4-I^3+I=1$$.

• Could you (or one of the 22 upvoters) explain the last step to me? – user1717828 Mar 21 at 1:35
• @user1717828 $I$ is the Roman numeral for $1$, so $I^4-I^3+I=1^4-1^3+1=1-1+1=1$. – noedne Mar 21 at 2:03
• Ahh!! I did the complex math out like three times before submitting to Google to confirm I wasn't crazy. No idea what I was thinking. Thanks! – user1717828 Mar 21 at 10:46

The rot13 translation of "one" is "bar". The only connection between "bar" and 505 that I could find is this very obscure definition given in urban dictionary (which was entry #4 and has more downvotes than upvotes), which says that it's slang for getting a drink at a bar with friends after work. Perhaps it's a really old outdated slang term, which is why your grandpa used it.

• Beer O'Clock, Can't be any different to 4:20 or the Masonic arguments pertaining to yardarms or the time of day, It's beer O'Clock somewhere in the world. In the olden days 505 meant OOO. We left at 5pm. – mckenzm Mar 21 at 5:42

Elaborating on @hexomino answer 505 -> DV.

Is it possible that:

I want to DownVote you 505 times which was odd number resulting 1 DV.
var num=505; isOdd(num); function isOdd(num) { return num % 2;}
I'm not downvoting you.

Use the digital radix: 5 + 0 + 5 = 10, 1 + 0 = 1

• And where is Rot13 used? – Chronocidal Mar 19 at 15:58

If you use a "fivethousandfiftydecimal" base then 505 in this base is equal to 1 in decimal base. Just like 12 in octal base is equal to 10 in decimal base.

• Welcome to Puzzling.SE! I like the lateral thinking in this answer, but I'm afraid it doesn't quite answer the question, since it doesn't use rot13. – Brandon_J Mar 21 at 13:27

Working out possible solutions using rot13 and trig:

I feel gross and like I'm doing something wrong doing this but:

505 = 5 * 101 => V * CI

Then you:

rot13(V * CI) = I * PI => i * pi (getting pi honestly is the only reason I think this might be the right direction.

Here's where the rot13(gevt) comes in I guess? Not sure where to proceed from there.

• rot13 of I is not I. – Rubio Mar 20 at 20:53
• Well I'm an idiot. – Nick Vitha Mar 20 at 21:05

Tongue in cheek answer - technically works anyhow ;-)

050/5 rdhnyf 6/5 gurersber 050 rdhnyf 6. "Cebirq" hfvat zngu xabjyrqtr naq ebg68, nf erdhrfgrq ;-)

Rot13 a_zA-Z0-9