Kinesys materializes behind a huge stone 5, a few steps from the Archive of Numbers, the most heavily guarded building on Numerion. “Down, everybody down,” Liz whispers, pushing Dord behind the curve of the digit. “Somebody’s watching the entrance.”
Sure enough, a little farther off, a spy in a checkered trench coat is taking notes. M00N, whose universal translator is always on, turns everything the guards say into English, word for word.
Dord watches the scene with his arms crossed: “That spy is reasoning in a pitifully sloppy way. This will end badly.” Liz rolls her eyes: “You always think everything will end badly.” This time, though, Dord is right.
The Riddle
A spy is trying to figure out the rule that pairs the password with the countersign at the entrance to the Archive of Numbers. Hidden behind a giant digit, she watches the door.
A Numerian arrives and knocks on the great door, and a voice from inside says “twelve”; the Numerian answers “six” and is let in. A little later another Numerian knocks and is told “six”; he answers “three” and walks in.
At this point the spy is sure she’s figured it all out: she walks up, knocks, hears “four,” answers “two”… and the alarm goes off: the guards catch her on the spot. Why?
(Of course, there are infinitely many possible answers: we want the one that takes the fewest words to state.)
Hint
“Divide by two” fits every exchange the spy observed, but it isn’t the only possible rule. Try spelling out the passwords.
Solution
The right answer would have been “four,” because the word “four” has four letters: it is the only English number word that is its own countersign.
In every exchange observed, the countersign was the number of letters in the password: “twelve” has 6 letters and “six” has 3. The spy assumed she just had to divide by two, but for “four” the two rules give different results.
As we said, infinitely many rules fit the examples, but this is the one that takes the fewest words to state. Dord, naturally, figured it out right away. And he keeps reminding everyone.