We are presented with a long list of numbers followed by an unusual diagram. Ignoring the image for now and looking only at the numbers, most of them seem to be huge, and many end in a lot of
zeroes. One of the first things any mathematician should do when presented with such numbers is factorise them into their prime components (which is hinted at by the title, This combined with the fact some numbers are separated by punctuation implies each number represents a word, and its factors somehow represent letters (all prime factors fall between 1 and 26 inclusive - the range of the alphabet - and the 17th letter is Q, a fairly rare letter). So how does this encoding work exactly? Evidently we can match up primes with their corresponding letters, so 2 is B, 3 is C, 5 is E, etc. But this leaves out the letters corresponding to composite numbers. Since there's no good reason to assign the sixth letter F, say, to any one particular prime, the logical conclusion is that F would be associated with both 2 and 3, its own prime factorisation. This mapping is supported by the fact there are usually many instances of each prime per factorisation (i.e. the indices are very high), so it's likely primes are representing more than one letter each. Also supportive of this mapping is the fact 1 appears by itself a few times, which makes sense as the number representative of A. This still hasn't quite solved the problem though, as our indices are still far too high. The trick here is to realise that each index is in fact being used to Now that we have the encoding rule, decoding the given numbers is a pretty fun logical exercise (assuming you didn't brute force it with a program, which is of course acceptable but far less enjoyable!). Some of the longer numbers aren't feasible to decode by hand, but luckily almost all of them are predictable and then checkable based on context. The lines when decoded give clues which seem to describe distinct words, and working out the synonyms here is aided by realising the fact they're arranged in alphabetical order. Putting this all together we get:
Some of these answers may still be too difficult to work out despite their clue and relative alphabetical position, but we should be able to rectify this upon discovering the next step. So far all we have done with this new code is decypher numbers with it; perhaps now we should try encyphering the new words we've extracted. Doing so should give a good idea of what's going on:
So in fact we have found eight pairs of words that share the same encoding. Promisingly, there are eight pairs of squares in the supplied image. There doesn't seem to be any good way to distribute the words/numbers though, so it seems we might still need to use the words somehow beforehand. The numbers have linked phrases like Belgian/holing, cartilage/turf out, and coldly/job-lot, but is there any other property that links them? The trick here is to spot that for each pair, exactly one letter appears in the same position in both words (ignoring punctuation). So BE
These letters seem like they could anagram to something, and indeed putting the numbers in ascending order gives us the word
Some of the words and phrases were a little more obscure than we would have liked, but hopefully the clues and backsolving were enough to get them all, or at least the majority. In some cases nicer pairs could have been used (inheriting/roadrunner was my favourite), but this would have made the puzzle too tricky or sacrificed the ordering-by-numbers step, which we believed was important for justifying the puzzle theme. Another reason the image was added was so that teams that wrote up a code to solve this puzzle were not given too much of an advantage over those that didn't. We were very aware that if teams decided to program something to solve this puzzle, they could solve it faster than expected, and so while we tried to mitigate this as much as possible, this was essentially the only reason Composites wasn't labelled 5-stars. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

The answer is: cofactor |
---|