Beanboozled Again

On the Subject of Beanboozled Again

When a joke goes too far...

The module shows a display with 8 encrypted characters. There are also 8 octagonal bean buttons also containing encrypted characters. In order to solve the module, press 5 beans in the right order and at the right times.

Section 1: Decrypting the display

The display is encrypted in beanzleglyphs. Look up their corresponding base-36 character in the lookup table below.

Beanzleglyph Lookup Table
1
	2
		3
			4
				5
					S	5	Ø	J	8	X
					O	W	Z	1	H	F
					V	M	Q	4	E	L
					3	D	T	C	6	U
					G	N	2	R	A	Y
					P	9	K	I	B	7

The message given is still encrypted. It is one of the words on page 2, however random letters were removed until the word length is 8, then it has been shifted randomly and then it has been encrypted using Turntriangle Cipher with a random coefficient array C, consisting of three coefficients ranging from 0 to 2. These values will be labeled C₁, C₂ and C₃ respectively.

Section 1.1: Turntriangle Cipher

Look up your character to encrypt in the cipher triangle (page 2) and call its position the pivot. Rotate your pivot clockwise 120 degrees around the center of the 6×6 triangle an amount of times equal to C1. Split the 6×6 triangle up into four 3×3 triangles. Rotate your pivot clockwise 120 degrees around the center of the 3×3 grid your pivot is in an amount of times equal to C2. Split the 6×6 triangle into nine 2×2 triangles and rotate the pivot around the center of the 2×2 triangle it is in by 120 degrees an amount of times equal to C3. Your new position is the encrypted letter.

Once you finish decrypting the display, take the value in the table below, corresponding to the encrypted word. This value will be labeled D.

Phrases
BEANBOOZLED	BEANEDAGAIN	BAMBOOZLING	TOOCOLOURFUL	BEANINGS	HYPERBEANS	ULTRABEANS	COOLBEANS
11	12	13	14	15	16	17	18
ROTTENBEANS	JELLYBEANS	LONGBEANS	LOBEANTOMY	NOTGOODBEAN	SAUCYBEANS	BAKEDBEANS	BEANOVERLOAD
21	22	23	24	25	26	27	28
BEANCIPHER	AMBEANGUOUS	BURNEDBEAN	KILLERBEAN	INEDIBLE	SURELYNOTCORN	BEANKRUPT	SUPERMARKET
31	32	33	34	35	36	37	38
GROCERIES	ROWANATKINSON	MEANDTHEBOYS	AT3AMLOOKING	FORBEANS	DANSBEANS	POGBEANS	BEANSANITY
41	42	43	44	45	46	47	48

Section 2: Calculating your bean values

Use the Beanzleglyph Lookup Table to give every bean two base-36 values. One for each orientation. Convert to base-10, add the values together and modulo 36 to get your I_n value where n is the bean in reading order. Now use BeanF--- on this array. Start at the position matching the last digit of your D value. Always modulo 36 after applying an action. The BeanF--- commands are given by the display colours in reading order in two rows. Then look up the character corresponding in the BeanF--- table. Use the colours position in the sequence, where necessary subtracted 8 from until within range of 1–8, for the row.

Section 2.1: BeanF---

<, >: Moves left/right 1 in the array, looping around.
+, -: Adds/Subtracts 1 at the current position.
[, ]: Start/End of a loop. Runs the loop code twice.
,, .: Retrieves the value at the current position and puts it in memory/Sets current position to the stored value (doesn’t if there is none).
←, →: If there is a smaller value directly on the left/larger value directly on the right, moves left/right, looping around.
↑, ↓: If this value and its cyclic opposite in the array share/don’t share odd-even parity adds/subtracts 1 at the current position. The cyclic opposite is the item 4 to the left/right of the current item.
*: Stores position and swaps with the new position as soon as it appears again, then resets memory.
∴, ∵: Encrypts/decrypts the current value using C.

BeanF---
	Ol	Bn	Lf	Yk	Ac	Li	Gd	Pe	Yl	Bd	Be	Mi	Le	We	Wt
1	<	>	+	-	[	]	,	.	←	→	↑	↓	*	∴	∵
2	>	,	-	↓	↑	∵	]	+	→	←	*	.	∴	<	[
3	-	→	*	←	↑	.	<	+	↓	>	]	∴	[	,	∵
4	→	↑	↓	[	>	∴	←	]	,	*	+	<	∵	-	.
5	∵	.	←	+	∴	-	↓	*	→	>	[	,	↑	<	]
6	]	>	←	[	→	↓	↑	*	∵	.	+	∴	-	,	<
7	,	↑	>	*	∴	→	<	[	↓	]	.	-	+	∵	←
8	←	→	-	↑	+	>	∴	∵	*	.	↓	<	]	[	,

Remove any loop characters that don’t have a pair, prioritising small loops. Call the n’th value of the array, which is your bean value, B_n.

Section 2.2: Calculating total

Take the n’th character of the display and take its set numbers using the row for the top half and the column for the bottom bean half. Concatenate them as top||bottom. Then append the sum of all four possible set numbers of the n’th bean. Modulo this by (B_n + 1) to get S_n.

Multiply S_n by all values of C concatenated interpreted as base-10 and add B_n to get your total T_n.

Section 3: Calculating bean presses

Press the bean with the sixth highest T value, up to the bean with the second highest T value, ordering ties with the latter in reading order being higher.

Section 3.1: The first four presses

Take the three colours of each bean and find their column index in the BeanF--- table where Bk = 0 and then from left to right, Ol = 1, Bn = 2, etc.. Multiply the value for the central colour by 241 and add the product of the other two colours to get a beans colour value V_n.

Press the bean when the following condition is true:

DigitalRoot([The bomb time in seconds] % (S_n + D)) = DigitalRoot(V_n)

Section 3.2: The final press

Look at the bean you pressed in the stage equal to the first digit of your D value. If it goes clockwise, R = 1. Otherwise, R = 0.