Solution to the Tiling puzzle

Tiling is one of the interesting puzzles of the Melbourne University Puzzle Hunt 2005 competition. It was part of the second act of the game and, according to the information on the game's website, as many as 11 people were involved in its creation. The puzzle was preceded by a short introduction that moved the script forward and served as a hint.

A sudden surge of inspiration hits you. Deciding to follow the ticket inspector’s instructions, you head down to platform 3 and board the crappy old train waiting there. Through the window extends a desolate landscape, with nothing but a single house that seems to be following you around, glaring at you with large, malevolent windows. Halfway to the end of the line, two figures dressed in black get on, and immediately start bickering about something or other. You recognise their voices from the strange conversation in Union House yesterday.

“Game’s over, it’s a draw, just drop it already.”

“You bloody cheater, I won that game.”

“No way, it’s all within the rules, nine times.”

“Wait, where’s that freaking ticket inspector?”

“I bet if he were here, he’d agree with me; it’s a draw.”

“Oh, shut your trap, Chan!”

With that, the shorter of the pair hurls something at his companion’s head. The taller man manages to jerk his head out of the way at the last moment, and the hurled object flaps violently in the air as it flies across the carriage, bounces off a window and lands on the seat next to you. While avoiding being struck in the head, however, Chan overbalances and crashes to the floor, spilling the contents of a small fabric bag as it flies from his grasp.

“Now look what you’ve done!” his companion shouts at him. “None of them had better be broken, you idiot!”

Muttering curses under his breath, the shorter man stoops to help his colleague collect from the ground what appear to be small ceramic floor tiles. As the two men put them back in the bag, they count and check them carefully, and as they do so you notice unexpectedly that the tiles have small letters glazed onto their surfaces.

When the two men are done, they stamp off to the other side of the carriage, still bickering, leaving you to pick up from the seat next to you what turns out to be a notebook.

Solution

Judging by the introduction and the contents of the notebook, Chan and White were playing Scrabble. Thus, the puzzle asks to reconstruct their game based on the final table. To do this, for each move made, you should place the word listed in the table onto the board in a way that yields the corresponding number of points, while also accounting for the remaining letters available for the players to use. While there are multiple possible placements on the board for most of the words in the table, there is only one way to solve the whole problem.

Below you can see the filled-in board corresponding to the table, resulting from placing the first word (you) either horizontally or vertically, as well as the number of letters that remain unused at that point.

Horizontal position of the first word

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Vertical position of the first word

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Remaining letters

Letters	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z	*
Amount	0	0	0	0	1	0	0	0	2	0	0	0	1	1	3	0	0	2	0	0	0	0	0	0	1	0	0

To continue solving the puzzle one should refer back to the introduction. At the end of the table the gap between the players was 239 points in White's favor. However, their conversation indicates that the scores were tied after Chan's next move. It also suggests that Chan placed his word on two unoccupied red squares, causing its value to increase by 9 times.

Thus, the task can be formulated as follows: make a word using the remaining letters (E, I, I, M, N, O, O, O, R, R, Y) and place it on the two empty red squares so that it yields 239 points. The solution to this problem is shown below.

Horizontal position of the first word

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Vertical position of the first word

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Chan formed the word "oxymoron", which, after taking into account all bonuses, earned him exactly 239 points. This word was the answer to the puzzle.