Solution to the Characterisation puzzle

Characterisation is one of the interesting puzzles of the Sydney University Puzzle Hunt 2010 competition. The plot of the game that year was based on Lewis Carroll's "Alice's Adventures in Wonderland" and "Through the Looking-Glass and what Alice found there". The game consisted of numerous scenes that were improvisations on the famous "A Mad Tea-Party". Each scene began with a short introduction that provided context for the task and could also contain some hints. Characterization was the last puzzle of the game before the final Meta Puzzle and was rated five stars out of five in difficulty.

These biscuits aren’t sweet enough. Pass the sugar, would you?” asked the Mad Hatter, and the March Hare pushed the pot over to him obligingly. He poured the sugar over the plate of biscuits as he continued.

“The Red Queen’s fixed, furious gaze faltered and tore from Alice’s back, for her nemesis was preparing to strike. Losing all composure, she turned to face the White Queen. ‘She is mine, and so is this place, sister!’ she cried as she lunged towards the White Queen, but stopped just short, realising what an error she had made. That little girl, the cause of so much strife, was now beyond her reach! The Old White King and the White Queen prepared to strike, as the brave knight stood by, powerless to stop them.”

The March Hare began dozing on his stool, and then began snoring loudly, his jowls flapping in his fitful rest.

“Hey, lazyface!” said the Dormouse, throwing the teapot at the rabbit’s head. It hit with a clang and soared into the air, and the March Hare sat up, wide-eyed with surprise, just in time for it to strike him again as it came back to earth. Alice and the Mad Hatter laughed as the two creatures shot furious glances at each other over the table.

“Now now, my guests, we wouldn’t want Alice to think we’re mad, would we?” said the Mad Hatter, and though he sounded serious, it made Alice laugh even harder.

“Let’s see if she’s mad like us,” said the Dormouse. “Give it to her, Hare!”

The March Hare, now somewhat recovered, leapt beneath the table and retrieved a glimmering, colourful cube. He bounced it off the tabletop, and it landed perfectly in Alice’s lap. What on earth could this be?

After the end of the game the organizers provided a detailed solution to the task.

Examples of filling out the layers

First layer

1. (2, 1) = spade/?; (3, 2) = spade/?.
2. (4, 1) = heart/?.
3. (4, 4) = club/?; (3, 5) = club/?.
4. (3, 4) = ?/green; (2, 5) = ?/green; (4, 2) = ?/green.
5. (4, 2) = club/green; (3, 1) = club/?.
6. (3, 4) = triangle/green; (2, 3) = triangle/?; (2, 2) = triangle/?; (1, 2) = triangle/?.
7. (2, 5) = diamond/green; (2, 4) = diamond/?; (1, 4) = diamond/?.
8. (1, 3) = heart/?.
9. (5, 2) = spade/?.
10. (2, 1) = spade/red; (1, 2) = triangle/red; (1, 3) = heart/red; (1, 4) = diamond/red.
11. (2, 2) = triangle/purple.
12. (2, 3) = triangle/yellow; (2, 4) = diamond/yellow.
13. (3, 2) = spade/blue; (4, 1) = heart/blue.
14. (3, 1) = club/yellow.
15. (5, 2) = spade/purple; (5, 3) = ?/purple; (5, 4) = ?/purple; (4, 4) = club/purple.
16. (3, 5) = club/blue; (4, 5) = ?/blue.
17. (4, 3) = ?/yellow.
18. (4, 3) = heart/yellow; (5, 3) = heart/purple.
19. (4, 5) = diamond/blue; (5, 4) = diamond/purple.

Second layer

1. (1, 3) = triangle/?; (2, 1) = triangle/?; (3, 2) = triangle/?.
2. (1, 4) = heart/?.
3. (4, 2) = club/?.
4. (4, 4) = spade/?; (3, 4) = spade/?; (2, 3) = spade/?.
5. (1, 5) = ?/yellow.
6. (4, 3) = ?/purple; (3, 3) = ?/purple.
7. (3, 3) = heart/purple; (2, 2) = heart/?; (3, 1) = heart/?.
8. (4, 3) = diamond/purple; (5, 3) = diamond/?.
9. (3, 2) = triangle/green; (2, 2) = heart/green.
10. (2, 3) = spade/red; (1, 4) = heart/red.
11. (3, 1) = heart/blue; (4, 2) = club/blue.
12. (2, 1) = triangle/red; (1, 1) = ?/red.
13. (1, 1) = diamond/red.
14. (2, 4) = diamond/?; (1, 5) = diamond/yellow.
15. (3, 5) = club/?; (4, 5) = club/?; (5, 5) = club/?.
16. (3, 5) = club/purple.
17. (5, 3) = diamond/green.
18. (2, 4) = diamond/blue.
19. (4, 4) = spade/blue.
20. (3, 4) = spade/green; (4, 5) = club/green.
21. (5, 5) = club/yellow.
22. (5, 1) = triangle/purple.
23. (5, 2) = spade/yellow.
24. (1, 3) = triangle/yellow.

Third layer

1. (2, 4) = diamond/?; (3, 3) = diamond/?; (2, 2) = diamond/?.
2. (3, 1) = club/?; (4, 2) = club/?.
3. (4, 3) = spade/?; (4, 4) = spade/?.
4. (1, 3) = ?/red; (1, 2) = ?/red.
5. (3, 2) = ?/blue; (4, 3) = spade/blue.
6. (5, 5) = ?/green; (4, 4) = spade/green; (3, 4) = ?/green; (3, 3) = diamond/green.
7. (5, 3) = ?/purple; (5, 4) = ?/purple.
8. (5, 5) = club/green.
9. (3, 4) = heart/green; (2, 5) = heart/?; (1, 5) = heart/?.
10. (3, 5) = club/?.
11. (2, 3) = ?/yellow; (2, 2) = diamond/yellow, (1, 1) = ?/yellow.
12. (5, 1) = ?/blue.
13. (4, 1) = ?/red; (4, 2) = club/red.
14. (3, 1) = club/purple.
15. (3, 5) = club/yellow; (2, 5) = heart/yellow.
16. (4, 1) = heart/red.
17. (3, 2) = triangle/blue.
18. (5, 1) = diamond/blue.
19. (2, 4) = diamond/purple.
20. (1, 5) = heart/blue.
21. (5, 3) = triangle/purple.
22. (5, 4) = heart/purple.
23. (1, 1) = triangle/yellow; (1, 2) = triangle/red.
24. (1, 3) = spade/red; (2, 3) = spade/yellow.

Fourth layer

1. (1, 2) = triangle/?; (2, 3) = triangle/?; (3, 2) = triangle/?.
2. (2, 2) = club/?; (1, 1) = club/?.
3. (2, 5) = diamond/?.
4. (4, 3) = spade/?; (4, 4) = spade/?; (5, 5) = spade/?.
5. (2, 4) = ?/blue; (1, 5) = ?/blue; (4, 4) = spade/blue.
6. (4, 2) = ?/yellow.
7. (3, 2) = triangle/blue.
8. (2, 5) = diamond/yellow.
9. (2, 1) = diamond/?.
10. (1, 2) = triangle/yellow; (2, 2) = club/yellow.
11. (4, 2) = heart/yellow; (5, 1) = heart/?.
12. (4, 1) = spade/?.
13. (3, 3) = diamond/?.
14. (5, 2) = diamond/?.
15. (3, 3) = diamond/purple; (4, 3) = spade/purple; (5, 4) = ?/purple.
16. (5, 1) = heart/purple.
17. (5, 4) = triangle/purple.
18. (4, 5) = heart/?.
19. (1, 4) = heart/?; (1, 5) = heart/blue.
20. (2, 4) = club/blue; (3, 4) = club/?.
21. (2, 3) = triangle/red; (1, 4) = heart/red.
22. (3, 4) = club/green; (4, 5) = heart/green.
23. (5, 5) = spade/red.
24. (1, 1) = club/red; (2, 1) = diamond/red.
25. (4, 1) = spade/green; (5, 2) = diamond/green.

Fifth layer

1. (1, 2) = triangle/?; (2, 2) = triangle/?.
2. (4, 2) = diamond/?; (4, 3) = diamond/?; (5, 3) = diamond/?.
3. (4, 5) = heart/?.
4. (2, 1) = ?/red; (3, 1) = ?/red.
5. (2, 5) = ?/blue.
6. (4, 1) = ?/yellow; (3, 2) = ?/yellow; (2, 3) = ?/yellow; (2, 4) = ?/yellow.
7. (4, 4) = ?/green; (3, 4) = ?/green.
8. (2, 4) = triangle/yellow.
9. (5, 4) = triangle/?.
10. (3, 5) = spade/?; (4, 4) = spade/green; (2, 1) = spade/red; (2, 3) = spade/yellow.
11. (3, 2) = club/yellow; (3, 3) = club/?; (3, 4) = club/green.
12. (1, 3) = club/?; (1, 4) = club/?.
13. (2, 5) = diamond/blue.
14. (3, 1) = heart/red; (4, 1) = heart/yellow; (5, 2) = heart/?.
15. (3, 5) = spade/purple.
16. (4, 5) = heart/blue.
17. (5, 2) = heart/purple; (5, 3) = diamond/purple; (5, 4) = triangle/purple.
18. (4, 3) = diamond/red.
19. (4, 2) = diamond/green.
20. (1, 2) = triangle/green.
21. (2, 2) = triangle/blue; (1, 3) = club/blue.
22. (3, 3) = club/purple.
23. (1, 4) = club/red.