Mites and Tites


Whilst perusing a book entitled "Puzzles Old and New (Illustrated)" I came across an amusing little item which I think adapts well to a caving context:-

It is a bank holiday weekend and 2 separate parties of 3 cavers each from the Frotteurs Caving Club meet in a constricted cave passage having each just negotiated very tight sections. By good fortune they find themselves in a section of passage just 7 body lengths long over which, with care, it is was just possible for a caver to pass another. The leaders of each party, being rather obstinate, and spotting an opportunity for an extra bit of "sport" realise that it is just possible for both groups to pass each other within the following constraints:-

(a) At no time can any caver crawl backwards.
(b) No caver can crawl past another unless a body length of passage is clear beyond.
(c) Only 1 caver can move at any time.
(d) The total length of passage available is 7 body lengths.
(e) A gap of 1 body length separates the 2 groups when the conditions are agreed.

With the aid of the diagram below see if you can deduce how the 2 groups were able to pass before continuing on their way.

Solution Next Edition.