Solutions for Act I Scene 3 - Delighted

For this puzzle, we are presented with a bunch of seven-segment displays which, as the title suggests, have been "de-light-ed". In particular, it can be seen that on each row there are some segments which are never lit.

Taking a guess that each display is a 2-digit number, we can work out the broken segments on each row and use this information to figure out the original numbers. However, it can be quickly realised that sometimes this cannot be done uniquely. For instance, if the centre segment is broken, it's impossible to distinguish between a 0 and an 8.

The next step is to realise that each row actually forms some sort of number sequence. For example, the 5th row is clearly "1, 1, 2, 3, 5, 7, 11, 15, 22", which can be recognised as or searched online (possibly using the On-Line Encylopedia of Integer Sequences) to discover that these are the partition numbers. Assuming that each sequence is "nice" or common allows us to work out the rest of the numbers.

Since these are number sequences, the intuitive step is then to take the next numbers of each sequence. Recalling that our displays started off broken, removing the broken segments from the numbers gives a message.

The message reads "LIGHT UP PUZZLE ALSO CALLED?", referring to the puzzle Light Up by Nikoli. The puzzle is known as Akari on their English site, giving us the answer.

Design notes:

Sometimes puzzle ideas come from the most ordinary of places, with this one stemming from a broken timer on a soup boiler. Occasionally I'd try to read the timer, only to realise that there were multiple possible times the timer could be on, but I'd always be able to work out the true time by waiting a minute.

In terms of the puzzle, one member suggested having segments which were always on so that nicer sequences could be chosen (the final setup relied heavily on numbers with 8s). However, the theme of "lighting up" what's broken was too good to drop.

The answer is: akari