Lewis Carroll's Games and Puzzles

I used to have a paperback book devoted to various brain teasers by Lewis Carroll, which I foolishly jettisoned when it started disintegrating and have never been able to find again after many online searches.  I associate it with the place we lived in 1986-1991, so it was probably published no later than that (quite possibly much earlier) and seem to recall it was edited by Martin Gardiner.  It may have been published by Penguin.  And yes, I have used some and all of those search elements and more (including quotes from specific rhymes and puzzles I remember from inside the book) to no avail.

One of the games this book introduced me to is a thing where you are to change one word into another in a certain number of steps, changing one letter at a time - and of course, each step must be a word. 

For example, the challenge might be to change DROP into PAIL, which can be done in 6 steps as follows:
DROP
DRIP
GRIP
GRIN
GAIN
PAIN
PAIL

(It may be possible to do it in fewer than six steps, that's just what it took me!)  This is a game I've played sometimes on the subway for fun, setting myself the odd semi-random challenge; ideally there is some connection between the words.

Other examples I generated, as a possible exercise for the reader: 

• change HAND into FOOT (5 steps or fewer)
• change NOSE into EARS (5 steps or fewer)
• change BALD into HAIR (4 steps or fewer)
• change NOSE into TOES (4 steps or fewer)
• change COOL into WARM (5 steps or fewer)
• change SHOE into SOCK (this took me 10 steps - surely it can be improved upon!)
• change MIND into MUSH (5 steps or fewer)