The Groupexpert series
This puzzle is self-explanatory. You will need to think of a neat way to encode the table of claims about who was what, and of saying that there is exactly one true entry in each line.
When I was a student (in the Good Old Days) ten guys in my group theory class decided to form a band, naturally called Permutation. Equally naturally, they never played in the same configuration twice. The effect was mathematically interesting, if musically regrettable.
At a class reunion recently, this conversation occurred:
“I remember that night. That’s when Harry was singing, with Frank on bass, Andy on the keyboard and Chuck on drums.”
“Me too, but you’re wrong about who was what. Dave was the vocalist and George played keyboards. You’re right about Frank, but the drummer was Andy.”
“You’re both wrong about Andy. He played bass….”
and so on. Six people tried to remember, and came up with six different claims which can be summarised in a table:
| Vocals | Bass | Drums | Keyboard | |
| 1 | Harry | Frank | Chuck | Andy |
| 2 | Dave | Frank | Andy | George |
| 3 | Dave | Andy | Bill | Iain |
| 4 | Ernie | Frank | Chuck | Iain |
| 5 | Bill | Chuck | Dave | Iain |
| 6 | Iain | Jim | Ernie | Harry |
It turned out that each of the six was right in exactly one respect out of the four.
Well?
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