Lamp Code: Deduce the Lamps
Read the puzzle
Four lamps sit in a row, each with an unknown value; a row shows the sum of its lit lamps. Lit lamps by position from the left: positions 3 and 4 show 3; positions 2 and 4 show 5; positions 1 and 4 show 9; positions 2 and 3 show 6. The last row has positions 1, 2 and 3 lit. What number does the last row show?
What number does the last row show?
Compare the rows showing 3 and 5: they share one lamp.
14
Lamps worth 8, 4, 2, 1 fit every row: 2 + 1 = 3, 4 + 1 = 5, 8 + 1 = 9, 4 + 2 = 6. So 8 + 4 + 2 = 14.
How to solve it
Call the lamps, from left to right, first, second, third and fourth.
Step one: compare rows that share a lamp. The row showing 3 uses the third and fourth lamps, and the row showing 5 uses the second and fourth. They share the fourth lamp, so the second lamp is worth 5 minus 3 = 2 more than the third.
Step two: use the row showing 6, which lights the second and third lamps. Two numbers that add to 6 and differ by 2 are 4 and 2. So the second lamp is 4 and the third is 2.
Step three: fill in the rest. From the row showing 3, the fourth lamp is 3 minus 2 = 1. From the row showing 9, the first lamp is 9 minus 1 = 8. The lamps are 8, 4, 2 and 1, the same doubling pattern as a binary code.
Step four: the last row lights the first three lamps: 8 + 4 + 2 = 14.
The usual wrong answer is 3, from counting three lit lamps and giving each a value of 1. Quick check: the four values fit every row, since 2 + 1 = 3, 4 + 1 = 5, 8 + 1 = 9 and 4 + 2 = 6.
