Three pairs of brothers went off for a day’s fishing and each pair caught the same number between the two of them. Anglers are not everyone’s first choice for guardians of truth, however, and what the fishermen said afterwards needs a pinch of salt. Each man said what three others had caught. To sort it out, you need to know that each always states his brother’s catch correctly but overstates his own and understates anyone else’s.

Alan said that he had caught ten, Ernie had caught eight and Fred just three. Bill reckoned Charlie had caught three, Dave four and Ernie ten. Charlie claimed nine for himself, eleven for Bill and just two for Fred. Dave said that Alan caught eight, Charlie six and Ernie seven. Ernie boasted of a catch of fifteen for himself, six for Bill and seven for Dave, whilst Fred modestly claimed seven for himself, twelve for Bill and six for Dave. Who really caught how many?