2 moves.
123 87 4

56
-------- = 5 moves.
E312 87 4

E
-------- = 9 moves.
87654321

Twenty-six moves in all.

88.--_The Eccentric Market-woman._

The smallest possible number of eggs that Mrs. Covey could have taken to
market is 719. After selling half the number and giving half an egg over
she would have 359 left; after the second transaction she would have 239
left; after the third deal, 179; and after the fourth, 143. This last
number she could divide equally among her thirteen friends, giving each
11, and she would not have broken an egg.

89.--_The Primrose Puzzle._

The two words that solve this puzzle are BLUEBELL and PEARTREE. Place the
letters as follows: B 3-1, L 6-8, U 5-3, E 4-6, B 7-5, E 2-4, L 9-7, L
9-2. This means that you take B, jump from 3 to 1, and write it down on
1; and so on. The second word can be inserted in the same order. The
solution depends on finding those words in which the second and eighth
letters are the same, and also the fourth and sixth the same, because
these letters interchange without destroying the words. MARITIMA (or
sea-pink) would also solve the puzzle if it were an English word.

Compare with No. 226 in _A. in M._

90.--_The Round Table._

Here is the way of arranging the seven men:--

A B C D E F G
A C D B G E F
A D B C F G E
A G B F E C D
A F C E G D B
A E D G F B C
A C E B G F D
A D G C F E B
A B F D E G C
A E F D C G B
A G E B D F C
A F G C B E D
A E B F C D G
A G C E D B F
A F D G B C E

Of course, at a circular table, A will be next to the man at the end of
the line.

I first gave this problem for six persons on ten days, in the _Daily
Mail_ for the 13th and 16th October 1905, and it has since been discussed
in various periodicals by mathematicians. Of course, it is easily seen
that the maximum number of sittings for _n_ persons is (_n_ - 1)(_n_
-2)/2 ways. The comparatively easy method for solving all cases where
_n_ is a prime+1 was first discovered by Ernest Bergholt. I then pointed
out the form and construction of a solution that I had obtained for 10
persons, from which E. D. Bewley found a general method for all even
numbers. The odd numbers, however, are extremely difficult, and for a
long time no progress could be made with their solution, the only numbers
that could be worked being 7 (given above) and 5, 9, 17, and 33, these
last four being all powers of 2+1. At