## 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)
000000
000111
001022
001133
010044
010155
011066
011177
100088
100199
101010A
101111B
110012C
110113D
111014E
111115F