Help me solve a moriarty riddle

June 20, 2015 10:11 AM

My 9 year old has a "choose your own adventure" type Sherlock Comic book, which has a (non essential for the adventure) riddle that we can't seem to be able to solve. I've tried googling and wolfram alpha, and am still stuck. Please Help

The riddle goes like this
if 1 = 1
2 = 5
3 = 28
4 = 164
Then
5 = ?

The riddle is presented as a "test left by moriarty"

(Not sure if it has any impact, but the book itself is in french)

Thanks for your help !

posted by motdiem2 to Sports, Hobbies, & Recreation (14 answers total)

Here is one way to do it, though it's not clear if this is what you were supposed to come up with.
posted by deadweightloss at 10:21 AM on June 20, 2015

Response by poster: Thanks for this, but I'm not sure it's the solution, because it seems to me it would be too hard for a 9 year old to get... (and the next number doesn't really make sense in context, but then maybe it shouldn't...)
posted by motdiem2 at 10:25 AM on June 20, 2015

It's interesting that it's growing approximately exponentially.

5/1 = 5
28/5 = 5.6
164/28 = 5.86
posted by Chocolate Pickle at 10:28 AM on June 20, 2015

Can you post a picture of the page?
posted by Hatashran at 10:31 AM on June 20, 2015

It's possible that it's not mathematical. The numbers could refer to page numbers or word positions within a page.
posted by pipeski at 10:34 AM on June 20, 2015

Response by poster: here's a picture

I'm thinking as well that it might not be mathematical. I'll check the page numbers and let you know.
posted by motdiem2 at 10:37 AM on June 20, 2015

I followed links from the page posted by deadweightloss, and it looks like it goes back somehow to Nicomachus' table. Perhaps the author of the puzzle wanted to use something like Pascal's triangle without the predictability of "oh look another Fibonacci puzzle".
posted by clawsoon at 10:37 AM on June 20, 2015

Best answer: This is not a satisfying answer, but maybe it's something really simple, like using the equivalence property, and 5 = 2.
posted by amarynth at 10:45 AM on June 20, 2015 [12 favorites]

It seems to be 1x1, then 2x2+1, then 3x3x3+1, then 4x4x4+100 which is kind of a pattern but not really
posted by KateViolet at 10:48 AM on June 20, 2015 [1 favorite]

Response by poster: That was it amarynth ! It leads to sequence number 2, which says "congratulations on solving Moriarty's riddle"

...not feeling particularly proud to have spent a couple of hours already thinking about this... but thanks hivemind !
posted by motdiem2 at 10:51 AM on June 20, 2015 [2 favorites]

Kateviolet has it!

You could say the first one is 1 x 1 +1, and there's the pattern!
posted by zorseshoes at 10:55 AM on June 20, 2015

Duh, i misread that comment completely. Maybe no more commenting when high.
posted by zorseshoes at 10:58 AM on June 20, 2015 [10 favorites]

This puzzle is sort of the equivalent of the "bus driver" puzzle/joke/prank that I was told as a kid. The answer is given at or near the beginning, but the rest is so distracting that it just goes past most people.

"You're the bus driver. At the first stop three people get on the bus. At the second stop two people get on, one person gets off. At the next stop..." [subject starts trying to write down the numbers] "X people get on, Y people get off..." and so on and on for a good long time, then suddenly ask, "Who's the bus driver?" Most people have long since forgotten that they are.

The bus driver one would only work verbally, but yours was a type that works in print. You're like Sherlock, trying to figure out the pattern, when Watson would say, "Oh! But he said 5=2."
posted by tomboko at 11:10 AM on June 20, 2015 [4 favorites]

Why 4x4x4+100 and not 4x4x4+1?
posted by SemiSalt at 12:40 PM on June 20, 2015