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Solutions for Act IV Scene 2 - Letters And Numbers

We seem to have been presented with two versions of an episode of the excellent Australian television show Letters and Numbers. In this gameshow, contestants are tasked with finding the largest word they can from a set of letters, and manipulating numbers with the four basic operations to reach as close to a target number as possible. Each game is concluded with a nine-letter anagram (typically presented as two smaller words) known as the Conundrum.

Closer inspection reveals the images and the transcript provided don't actually match up, and in fact must come from two different games (or episodes). Usefully however, the transcript provides just enough information to determine the letters and numbers supplied in each round. Even better, we have enough information to work out their ordering (with some forward thinking) and the number rounds' targets as well. These are as follows:

NOUPBMICE
TRIFMLEYF
2 4 6 8 7 8 (target 917)
TLUCVSHEN
HATBOXGEN
50 6 10 2 4 4 (target 687)
QMNOPRSTU
50 1 3 1 2 2 (target 335)
SHIN AFORE

It's also worth noting that the contestants in the transcribed episode are rather bad at the game overall. In fact, we can do much better! In particular, each letters round contains a unique longest word, while each numbers round has a unique solution. The Conundrum has two possible solutions, but the contestants' comments rules out one of them. The best plays are:

COMBINE
FIREFLY
((8*8*4+6)*7)/2
LUNCHES
HEXAGON
((50-4)*10-2)*6/4
NOSTRUM
(50-2)*(3*2+1)-1
REFASHION

These words and numbers don't seem very useful however. The key step here is to note that we now have a well-defined ordering of letters/numbers given any string of appropriate length. For example, extracting COMBINE from NOUPBMICE is done by taking the 8th letter from the original string, then the 2nd, and so on, written in shorthand as: 8265719. The only thing left to use is the supplied images, so what happens if we apply this extraction order to the first round's letters (RHASWEOTD)? Indeed we get THEWORD, which is extremely promising. The first letters of the images reading RECAPS and the Conundrum answer being REFASHION were also meant to hint at this next step. Continuing in this way gives:

THEWORD
INWHICH
51/50
YSLASTN
AMEISIN
150
UDEDITS
8
CHARSLONG

Reading the first two number answers as Roman numerals (so LI/L and CL respectively), we find the following message: The word in which Lily's last name is included (it's 8 chars long). This refers to Lily Serna, one of the cohosts of the show, and so our answer turns out to be the only 8-letter word containing SERNA as a substring, namely USERNAME. Note we used a letter puzzle on the numbers lady's name to reach our final solution, and that a username typically includes both letters and numbers, thus tying into the theme and confirming the answer.


Design Notes:
It has been pointed out by Geoff Bailey of Playing Letters and Numbers that some of the word rounds in fact did have more than one optimal solution. Specifically: in the first round, an alternative seven-letter word is UMBONIC (relating to the bosslike centre of a disk), while in the second round, an alternative seven-letter word is METRIFY (to compose into verse). We're sorry for missing these, but trust most people should not have hit upon these without first spotting the more common words. In any case, these more obscure words don't result in any useful sort of message after applying the second step.

The answer is: username