We gave, a week or two ago, two problems from Edward Wakeling's Rediscovered Lewis Carroll Puzzles (Dover, pounds 4.95). We are delighted to report that our readers have, in both cases, improved on Lewis Carroll's own solutions.

The simpler of the two was getting from GATE to OPEN, changing one letter at a time. Carroll's version was: GATE, date, dote, dots, does, dyes, eyes, eves, even, oven, OPEN. Several readers, however, have given: GATE, gats, oats, opts, opes, OPEN - but perhaps the Rev Dodgson's edition of Chambers did not list gat (old version of "get" or an American gun) or ope (old form of "open").

The other problem concerned a minimalist dinner party at which the Governor of Kgovjni invited his father's brother-in-law, his brother's father-in- law, his father-in-law's brother and his brother-in-law's father.

In Carroll's own solution, there is only one guest. The simplest family tree permitting this has three sets of marriages between cousins. The guest is his aunt's husband (who is thus his father's brother-in-law); his brother has married the uncle's daughter (making uncle his brother's father-in-law); his sister married the uncle's son, (making uncle his brother-in-law's father) and the governor himself married the daughter of his uncle's brother.

Several of our readers, however, have tied another branch in the family tree to how that there need be no guest at all. With the governor married to his sister's husband's father's widow, he becomes his own brother-in- law's father. And all the other relations too.

Who said family gatherings were dull?

Book prizes for the best solutions to both puzzles to: J Leech, Ian Kay, Christopher Godwin Adam Sobey, MJ Wilcock and Oliver Pereira.