Every weekday at a small radio station, somebody has to solve the same puzzle before ten in the morning, and they solve it on the back of a envelope.
The programme is sixty minutes long, and it is built out of exactly two things. Songs run two minutes each. Interviews run five. The running order can hold any mixture of the two, but the total must add up to sixty minutes, because at eleven o'clock the news begins whether the presenter has finished or not.
Yesterday's show had four interviews. Four interviews, each lasting five minutes, take twenty minutes of the hour, which leaves forty minutes of music — and forty minutes of two-minute songs is twenty songs. The production assistant wrote «4 and 20» on the envelope and went to make tea.
Today there are only two interviews scheduled. Ten minutes of talk leaves fifty minutes of music, which is twenty-five songs — five more records to find before ten o'clock.
What the assistant never does is guess. She is not choosing songs and interviews independently: the moment the number of interviews is fixed, the number of songs is decided for her, because the hour cannot stretch.
Two things follow, and she has both written on the wall. The answer is always a whole number — nobody broadcasts half a song. And there is a limit to interviews: twelve of them would fill the hour by themselves and leave a programme with no music in it at all.