Sources page biographical material

5.X.4. COUNTING CIRCLES
G. A. Briggs. Puzzle and Humour Book. Published by the author, Ilkley, 1966. Prob. 2/13, pp. 23 & 75. Pattern with hexagonal symmetry and lots of overlapping circles, some incomplete.
5.Y. NUMBER OF ROUTES IN A LATTICE
The common earlier form was to have the route spell a word or phrase from the centre to the boundaries of a diamond. I will call this a word diamond. Sometimes the phrase is a palindrome and one reads to the centre and then back to the edge. See Dudeney, CP, for analysis of the most common cases. I have seen such problems on the surface of a 3 x 3 x 3 cube. The problems of counting Euler or Hamiltonian paths are related questions, but dealt with under 5.E and 5.F.

New section -- in view of the complexity of the examples below, there must be older, easier, versions, but I have only found the few listed below. The first entry gives some ancient lattices, but there is no indication that the number of paths was sought in ancient times.

Roger Millington. The Strange World of the Crossword. M. & J. Hobbs, Walton on Thames, UK, 1974. (This seems to have been retitled: Crossword Puzzles: Their History and Cult for a US ed from Nelson, NY.)

On pp. 38-39 & 162, he gives the cabalistic triangle shown below and says it is thought to have been constructed from the opening letters of the Hebrew words Ab (Father), Ben (Son), Ruach Acadash (Holy Spirit). He then asks how many ways one can read ABRACADABRA in it, though there is no indication that the ancients did this. His answer is 1024 which is correct.

A B R A C A D A B R A

A B R A C A D A B R

A B R A C A D A B

A B R A C A D A

A B R A C A D

A B R A C A