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Easter the hotel was overcrowded; and five of us, including Eckenstein and  myself, were sleeping in 
the barn.  One of Eckenstein's greatest friends  was Mrs. Bryant, whose beautiful death between 
Chamonix and Montanvers in  1922 was the crown of a noble life.  She had brought her niece, Miss  
Nichols, who to intrepidity on rocks added playfulness in less austere  surroundings.  I formally 
accuse her of putting a kitten under  Eckenstein's pillow in the barn while we were in the smoking-
room after  dinner.  If it had been a cobra Eckenstein could not have been more upset! 
He had also an idiosyncrasy about artificial scent.  One day my wife  and a friend came home from 
shopping.  They had called at the chemist's  who had sprayed them with "Shem-el-nessim".  We saw 
them coming and went  to the door to receive them.  Eckenstein made one rush --- like a bull ---  
for the window of the sitting-rrom, flung it open and spent the next  quarter of an hour leaning out 
and gasping for breath. 
Eckenstein was a great connoisseur of puzzles.  It is extremely  useful, by the way, to be able to 
occupy the mind in such ways when one  has not the conveniences or inclination for one's regular 
work, and there  is much time to kill in a hotel or a tent in bad weather.  Personally, I  have found 
chess solitaire and triple-dummy bridge or skat as good as  anything. 
Eckenstein was a recognized authority on what is known as Kirkwood's schoolgirl problem, but we 
used to work all sorts of things, from problems  connected with Mersenne's numbers and Fermat's 
binary theorem to the purely frivolous attempt to represent any given number by the use of the  
number four, four times --- neither more nor less, relating them by any of  the accepted symbols of 
mathematical operations.  Thus: 
18 = 4 (4.4) + .4 
38 = 14 + . + 4 
106 = ł4 + 4.4 .4 
128 = 44ö4-Sq.Rt.of  4 
his has been done up to about 170, with the exception of the number 113, and thence to 300 or 
thereabouts with only a few gaps.  I solved 113 with the assistance of Frater Psi and the sue of a 
subfactorial, fur Eckenstein would not admit the use of this symbol as fair. 
He was also interested in puzzles involving material apparatus, one of which seems worth mention.  
He was in Mysore and a travelling conjurer sold him a whole bundle of more or less ingenious tricks.  
One of these consisted simply of two pieces of wood; one a board with a hole in it, the other shaped 
somewhat like a dumb-bell, the ends being much too big to go through the hole.   Eckenstein said 
that he was almost ready to swear that he saw the man take them up separately and rapidly put 
them together, 
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in which condition he had them and was never able to take them apart.  He explored the surface 
minutely for signs of complexity of structure but without success.  I never saw the toy, he having 
sent it to Mr. W. W. Rouse Ball, a great authority on such matters, but also baffled in this case. 
We were naturally always interested in any problems concerned with the working out of a difficult 
route, and here his probity on one occasion made him the victim of an unscrupulous child of 
Shaitan.  The villain appeared in the guise of an old and valued friend, saying "Is it possible to reach 
Q from P (mentioning two places in London) without passing a public house?"  Eckenstein accordingly 
took his walks in that direction and after endless trouble discovered a roundabout way which 
fulfilled the condition.  Communicating the joyful news, his friend replied, "Good for you!  Here's 
something else.  Can you get to the Horseshoe, Tottenham Court Road, from here without passing a 
public house?"  I do not know how many pairs of alpine boots Eckenstein wore out on the problem, 
before asking his friend, "Can it be done?"  A telegram assured him that it could.  More boots went 
the way of all leather and then he gave up. "It's perfectly easy," said the false friend, don't pass 
them --- go in!"