# Seven-Segment Display Puzzles

There are a lot of puzzles involving the seven-segment display of numbers and arithmetic. Since most of them differ by only a slight change in rules, there is almost no point in making separate articles for all of them. Thus, here is the list of such puzzles that have appeared on the WPC.

By the term "seven-segment display," we refer to the display style of digits shown below. Note that, in some puzzles, "7" is presented differently with an additional segment on the top-left. This type of numerical representation was patented by Carl Kinsley in 1903.[1] Application of such display for puzzlish matter existed for a long time; for example, the earliest instance of "Calculator Spelling" dates back to the 1970s.[2]

Example of the seven-segment display.

## List of puzzles

### Two Clocks

Example of Two Clocks. Solution: 00:03. Note that while there's an ambiguity on when the snapshots were taken, (one of the clocks from the 2nd snapshot can be either from 21:22, 21:23, 21:25 or 21:26) time difference can be determined uniquely.

From WPC 2016/Round 7.

Two digital clocks have been wired to one such display. Both clocks are going at the same pace but they are set to different times. The display now shows both times, one over another: a segment on the display is lit if at least one of the two displayed times uses that segment.

In each puzzle, you have a different pair of clocks. You are given several snapshots of the display, each taken at a different moment in time. Determine the difference between the times shown on the two clocks. (This difference is the same in each snapshot.) As the solution, express the difference in the form HH:MM, with the value being between 00:01 and 12:00, inclusive.

(Rules and example from WPC 2016 IB)

### Digital Scale

Example of Digital Scale. Solution: Apple = 74, Banana = 3.

From WPC 2016/Round 7.

We have some types of fruit. The weight of each piece of fruit is a positive integer. All pieces of fruit of the same type weigh the same. We have weighed some combinations of fruit on a scale with a digital display. The scale always shows the exact weight, but its display is faulty: some segments that should be on remain off. In each puzzle, the faults are consistent between weightings. Determine the weight of each fruit type.

(Rules and example from WPC 2016 IB)