# Melbourne University Mathematics and Statistics Society

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 Solution for 3.2 Build-A-Puzzle (Answer = LEMON)

As hinted by the title, the aim of this puzzle is to construct a puzzle rather than solving one. As such, this might inadvertently bias puzzle authors who understand the various challenges that take place when constructing a puzzle.

Three of these challenges are represented here:

1. Coming up with a thematic answer. This is not usually a difficult thing to do, unless the puzzle is highly constrained, or there are additional meta restrictions.
2. Coming up with an answer that fits the meta restrictions. In some cases the meta is so restrictive that there is only one possible answer you are forced to use.
3. Coming up with a clever extraction. Or even any extraction at all. Sometimes you may not already have all the letters you need.

Thus, the first thing to do is to come up with a good thematic answer that fits the meta! The only mythological creature whose first 5 letters are palindromic is the WEREWOLF, and this is hinted/confirmed by the choice of your name Remus. That's right, you are going to be Remus for the remainder of this solution.

Now, it is possible to spell WEREWOLF directly from the words, but as a good puzzle author you do want to use as many of these 11 items as possible (after all, you've spent countless hours drawing each individual image and don't want to waste any of them). You also like the idea of repeating a mechanism already used in an earlier step of the puzzle, namely synonyms. You go through a thesaurus and discover that LYCANTHROPE is a synonym of WEREWOLF which has exactly the same number of letters as the number of words we have. That's great news!

With that in mind, you proceed to actually work on the extraction step. You've opted to go with something as simple as just giving a number for each item. Or rather, Adib has suggested this, and you trust that he always knows what's best for the puzzle. Usually anyway. It turns that there is only one way to do this to spell out LYCANTHROPE (lucky you!) with the set of words you already have:

New OrderIndexLetter
ELF2L
WYVERN2Y
UNICORN4C
FAUN2A
DEMON5N
GHOST5T
PHOENIX2H
DWARF4R
GOLEM2O
IMP3P
PIXIE5E

Finally, the puzzle is done! So you scribble down the numbers 2,2,4,2,5,5,2,4,2,3,5 on the page and send it for test-solving.

But aren't you a silly goose - you've forgotten to actually reorder the images to match this new order! Indeed, when the test-solving comes back, the tester asks to confirm whether the answer is LEMON.

This leaves you very confused, so you decide to double-check your work. Indexing into the words using the original order:

Old OrderIndexLetter
FAUN2A
UNICORN2N
GHOST4S
DWARF2W
PIXIE5E
WYVERN5R
ELF2L
GOLEM4E
IMP2M
PHOENIX3O
DEMON5N

This gives you the final answer LEMON. You chuckle at the notable irony that this answer is not thematic in any way to the puzzle.

Author's Notes:
The puzzle is based on an idea that had been floating around for a couple of years. Often, the challenge for constructors is to use the list of items they have and think of a clever extraction. In some cases, if the list of items is too restrictive, it may be difficult to come up with a good thematic answer, even if the extraction is as simple as indexing a single letter from each word. This puzzle has gone through many reductions in difficulty, including explicitly telling the reader to find a thematic answer first, as well as hinting towards WEREWOLF by means of the recipient's name Remus. At the end of the day, we still thought the puzzle was fairly tricky, but we couldn't really reduce the difficulty any further without removing the 'aha' completely.