Rules
Perfect Number was the ace selection game in University War. Players saw a screen of sentences, each counting a digit on the same screen, and had to find the numbers that made every sentence true.
The box
The dashed box holds seven sentences and a short box code. Each sentence reads “The digit d appears __ times”, for seven different digits. A sentence is true when the blank holds exactly how many times its digit appears anywhere in the box.
What counts
- The digit printed in each sentence (so every digit with a sentence appears at least once).
- Every digit of the box code.
- Every number you write in a blank.
Our version
- The show’s exact sentences were not published, so every box here is generated: seven different digits from 1 to 9, and a box code of 4 to 8 digits.
- Every blank takes a number from 1 to 9.
- A solver checks every possible filling. Only boxes with exactly one true filling are used, and at least one blank is 3 or more.
- Check needs every blank filled. It reports how many sentences are false, not which. A wrong check adds 10 seconds to your time.
- You can give up and see the true box.
- The Daily box is the same for everyone each day.
Strategy
Start with the base count. For each sentence, count its digit in the sentence itself and in the code. The answer is that number plus how many blanks end up holding that digit.
Most answers are small. With seven blanks, only a few can be large. Expect lots of 1s and 2s, and remember that every 1 or 2 you write changes the count of the 1s and 2s.
Fix the digits nobody writes. A digit like 8 or 9 rarely appears as an answer, so its sentence is usually just its base count.
Change one blank at a time. Each change moves two counts: the number you removed and the number you wrote. Recount just those two sentences.