Christmas Maths Puzzle 2017 – The Solution!

Thanks to everyone who had a go at this. It was great to see such an enthusiastic response. In the end, there were two correct responses (and several near misses!). Credit for those solutions is given lower down.

Here’s the solution…

The first thing to do was to put the postcards into order (the two sets provided alternative clues to the same things). They were numbered in binary, from 0 to 7, with the red presents (“full”) representing 1 and the green ones (“empty”) representing 0.

Next, you had to interpret the postcards:

WOLF (from the UK version of Gladiators)

WOLF Blitzer (US Journalist/TV News Presenter)

RAM (Computer Memory)

RAM (Male Sheep)

150 (CLONE – ONE = CL)

150 (Clock showing time “One Fifty”)

WRAPPING Paper

WRAPPING Presents

The 39 STEPS (1935 Film)

The 39 STEPS (1978 Film)

÷ (Asterix and the Great Divide)

13

13 (Fourth Happy Number)

Samuel MORSE (Painter/Inventor)

Inspector MORSE (TV/Literary Detective)

Putting these clues together gives:

WOLFRAM 150 WRAPPING 39 STEPS ÷ 13 MORSE

WOLFRAM 150 refers to Wolfram Rule 150, a transition rule for an elementary cellular automaton. Wolfram’s rules operate iteratively on binary sequences, transforming them into a new binary sequence at each step.

[Rule 150 is actually quite straightforward in that each term of the new sequence is equal to the sum mod 2 of the corresponding term and its two neighbours in the current sequence.]

In the basic case, Wolfram’s rules operate on infinite sequences, but you can apply them to finite sequences if there is WRAPPING (both ends of the sequence are joined to form a loop).

Of course, we already have a finite binary sequence:

Once again, the red parcels represent 1s, while the green parcels represent 0s, giving:

0 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1

So we need to apply Wolfram’s Rule 150 to this sequence, treated as a continuous loop, for
39 STEPS ÷ 13 = 3 STEPS (I wanted people to have a fighting chance of doing this by hand).

The three steps are:

0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 00 0 0 1 1 1 0 1 1 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 11 0 1 0 1 0 0 0 1 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 1

That final sequence can be interpreted as MORSE code (based on the international standard):

… .. -..-

Which translates as…

SIX

So Elf Six is the guilty party!

The first to solve the puzzle was Matt Becker, who impressively posted a complete solution on the same evening that the challenge was set (so he only had the first set of postcard clues). Getting into the spirit of things, he even posted his answer in code (ROT13):

Click the image for the translation…

Apparently, he would have solved it even quicker, but he was watching TV:

The other correct solution was from Neal/zbvif:

Neal submitted a number of comments showing his earlier working, but since I censored them all for spoiler reasons, I no longer have them to show here! You can see what’s left of them on the puzzle page though.

Congratulations to Matt and Neal!

Well done also to Sara, Troy, William, Alex, Andy and Heather, for varying degrees of proximity to the solution, ranging from “heading in the right direction” to “searingly, excruciatingly close” (see their comments on the puzzle page).

Merry Christmas Everyone!

If you’re interested in our book on the Maths of Christmas, it’s available by clicking on the image. US edition here.

Matt Becker’s Solution – Translated

The postcode clues represent:
THIRTY-NINE (The Thirty-Nine Steps)
THIRTEEN
DIVIDE (Asterix and the Great …)
RAM (Some computer memory)
MORSE (Samuel Morse)
ONE-HUNDRED-AND-FIFTY (“CL” in Roman Numerals, i.e. CLONE without ONE)
WRAPPING (Paper)

The boxes on the postcards specify the order of the clues via binary encoding (Red = ONE, Green = ZERO). The postcard clues in order spell out: WOLF RAM ONE-HUNDRED-AND-FIFTY WRAPPING THIRTY-NINE DIVIDE THIRTEEN MORSE.

Solution:
The trail of twenty-five boxes is the initial state of a one-dimensional cellular automaton (Red = ONE, Green = ZERO). Apply WOLFRAM’s rule ONE-HUNDRED-AND-FIFTY with WRAPPING of the first and last cells for three iterations (THIRTY-NINE DIVIDE THIRTEEN). The resulting pattern of dots and dashes spells out SIX in MORSE code.

2 thoughts on “Christmas Maths Puzzle 2017 – The Solution!”

1. Olaf Doschke

Ouch. I didn’t give this one much time, but I didn’t think of sorting the cards by interpreting presents as three binary digit codes, though I partly noticed all possible permutations were there. I tried to match every three parcels to a position within the whole path, but there are no unique positions, so there would be several ways to try out.

I got some clues mainly by using google image search, which helps not knowing some things, which may be familiar for Britains. I got Wolf that way, for example, I also got 39 steps. Figuring out 13 was perhaps the easiest one, and figuring out the English title of that Asterix comic book for “Der Große Graben” was “The Great Divide.”

I had the feeling it would include 39 divided by 13=3 as some part of it, maybe an overall more extended calculation giving the elf number, eventually.

For some pics I thought of the wrong term, for example, I instead thought of SD RAM or SD perhaps puzzling into further letters to form a word, just like I thought of CLONE-1 meaning CL, but it didn’t occur to me this was roman numerals.

How you would say clock times varies a lot; even within Germany, some would say “10 to two”, some would say (roughly) “three quarter two”. “one fifty” is another possibility, but the military time of saying one hundred fifty is not a thing in Germany. I didn’t think of the time itself at all, though, I just had the clock in mind for that card.

RAM at least became more apparent with the alternative card, but as I didn’t even get the sorting idea, I didn’t reach further clues you got from combinations.

To summarize: No, this isn’t ranting, this is just pointing out I still had some fun in puzzling about this, and it might be amusing enough to hear about how successful you misled me.

Congrats to those figuring it out.

2. Heather Dudek

Very clever! I feel like a few more months and I would have gotten it. Thanks for the fun, and Merry Christmas!