On the Subject of 4 Lights

Binary turns them off...

A: 4-digit binary number, left to right. (Lit = 1)

B: 4-digit binary number, bulb label 1 to label 4. (Lit = 1)

(e.g.) on4, off1, on2, on3: A = 1011₂ and B = 0111₂

Shorthands

• ind: indicators
• #: number of
• label: the button with label/number

IF (1st that apply):	THEN press
ALL bulbs on	label 1,2,3,4
ALL bulbs off	label 4,3,2,1
#Lit bulb = #lit ind AND #Unlit bulb = #unlit ind	1) label (#lit) 2) label (#unlit)
1 lit bulb	*label of lit position
A = B	1) button below of leftmost lit bulb 2) smallest label whose bulb is lit
A ≥ 10 AND B ≥ 10 (in base 10)	C = A AND B **Press: position where C is 1 (left to right)
ELSE	1) lit labels: ASC 2) Unlit labels: DESC

* (e.g.) bulb at pos 3: press label 3

** A = 1101; B = 1011; then A AND B = 1001, pressing 1st then 4th in reading order.

Appendix BA5E: Conversion in base 2, 10 and 16

Binary (base 2)	Decimal (base 10)	Hexadecimal (base 16)
0000	0	0
0001	1	1
0010	2	2
0011	3	3
0100	4	4
0101	5	5
0110	6	6
0111	7	7
1000	8	8
1001	9	9
1010	10	A
1011	11	B
1100	12	C
1101	13	D
1110	14	E
1111	15	F