Lamp Code
Read the puzzle
Rows of four lamps show numbers. Each lamp is worth double the lamp on its right. Only the rightmost lamp lit shows 1; only the third lamp lit shows 2; only the second lamp lit shows 4. The bottom row has the first, third and fourth lamps lit and the second lamp off. Which number does the bottom row show?
Each lamp is worth double the lamp on its right. Which number does the bottom row show?
From the right, the lamps are worth 1, 2, 4 and 8.
11
The lamps are worth 8, 4, 2, 1. Lit: 8 + 2 + 1 = 11.
How to solve it
Give each lamp its value first. The examples show the rightmost lamp is worth 1. Each lamp is worth double the one on its right, so moving left the values are 1, 2, 4 and 8. Read from left to right, the four lamps are worth 8, 4, 2 and 1.
Now look at the bottom row. The first lamp (8) is lit, the second lamp (4) is off, the third lamp (2) is lit and the fourth lamp (1) is lit. Add only the lit lamps: 8 + 2 + 1 = 11.
Check the idea against the given rows: the second lamp alone shows 4 and the third alone shows 2, which fits the values 8, 4, 2, 1. With all four lamps lit the row would show 8 + 4 + 2 + 1 = 15, the largest number four lamps can make.
The common wrong answer is 13, from reading the lamps left to right as 1, 2, 4, 8 and adding 1 + 4 + 8. Another slip is 3, from simply counting the lit lamps.
This is how binary numbers work: the bottom row reads 1011, which is 11. Takeaway: give every position its value, then add only the ones that are switched on.
