Dim or Bright
Read the puzzle
Three lamps sit in a row. Each can be off, dim or bright, and bright counts double dim. Each row shows a total. Row 1: left dim, others off, equals 9. Row 2: middle bright, others off, equals 6. Row 3: left off, middle dim, right bright, equals 5. Last row: left bright, middle dim, right dim. What number does the last row show?
What number does the last row show?
First find each lamp's value: the top row gives the left lamp.
22
The top 3 rows give lamp values 9, 3 and 1. Bright counts double: 18 + 3 + 1 = 22.
How to solve it
Step one: find each lamp's dim value, one row at a time. The top row lights only the left lamp, dim, and shows 9, so the left lamp is worth 9 when dim.
Step two: the second row lights only the middle lamp, bright, and shows 6. Bright counts double, so the middle lamp's dim value is 6 divided by 2 = 3.
Step three: the third row has the middle lamp dim, worth 3, and the right lamp bright. The total is 5, so the bright right lamp is 5 minus 3 = 2, and its dim value is 2 divided by 2 = 1.
Step four: read the last row. The left lamp is bright, so 9 times 2 = 18. The middle lamp is dim, 3. The right lamp is dim, 1. The total is 18 + 3 + 1 = 22.
The usual wrong answer is 13, from adding 9 + 3 + 1 and forgetting that the left lamp is bright in the last row. Another slip is 23, from taking the right lamp as 2 in row 3 without halving it. Quick check: the dim values 9, 3 and 1 each triple from right to left, a neat pattern for a three-state code.
