Fantasy Logic League - Solutions for Round 3

[I] Here the key piece of information is that if only you knew how many theories were correct, you could deduce the answer. If the Bursar were the killer, then three theories are correct. And no other number of correct theories yields a unique solution. (Work out the cases, one by one). So, alas, it must have been

The Bursar

[J] Since the tarboosh is bigger than the graecist's hat, which is at least as big as the latinist's, the tarboosh must be the biggest hat. Whereupon since the puggree is bigger than Dust's hat, we can deduce

Tarboosh > Puggree > Shako

                                    Dust

But the historian's hat is bigger than Chalk's, yielding

Tarboosh > Puggree > Shako

                    Chalk       Dust

History

And then the rest is easy to fill in:-

Fustian teaches History and affects a tarboosh.

Chalk teaches Greek and wears the puggree.

Dust teaches Latin and ponces around town in a shako.

[K] The only solution consistent with the information given is that

Locke is The Master, Stock is the Bursar, and Barrel is the Chaplain.

Anyone who thinks that this gets the kinship relations in a twist must have forgotten that Chaplains can marry any number of people without thereby becoming married to them.

[L]                               98765

A matter of adding up the bits of information. If we lay out the various tries in columns, then each column contributes to the total of correct numbers as follows:

First column: 1 correct number

Second column: 0 or 1 or 2 correct numbers

Third column: 0, 1, 2 or 3 correct numbers

Fourth column: 0, 1, 2 or 3 correct numbers

Fifth column: 0, 1 or 2 correct numbers

But the third and fourth columns cannot both be contributing 3 correct numbers, because that would give us ??06?, ruled out by try number nine. So one of them contributes only 2, and every other column contributes the maximum number possible, because we need 10 correct numbers altogether. That means we have either ??02? or ??76?. But ??02? is ruled out by the sixth try, 52025. So it's ??76?.

And now the last digit cannot be a 1 (ruled out by 24751), so it must be a 5. That means we are down to ??765. The second digit must be 8 or 3, but 3 is ruled out by 73660. That means ?8765. And finally, any choice but 9 for the first digit is ruled out by one try or another.

-oOo-