The following special catch puzzle appeared in the issue of The Weekly Dispatch for All Fools' Day, 1900. It caused considerable amusement; for out of a very large body of competitors, many quite expert, not a single person solved it, though it ran for nearly a month.

" A race between a man and a woman that I happened to witness one All Fools' Day has fixed itself indelibly on my memory. It happened at a country-house, where the gardener and the cook decided to run a race to a point 100 feet straight away and return. I found that the gardener ran 3 feet at every bound and the cook only 2 feet, but then she made three bounds to his two. Now, what was the result of the race?"

A fortnight after publication the editor added the following note: "It has been suggested that perhaps there is a catch in the 'return,' but there is not. The race is to a point 100 feet away and home again—that is, a distance of 200 feet. One correspondent asks whether they take exactly the same time in turning, to which I reply that they do. Another seems to suspect that it is really a conundrum, and that the answer is that 'the result of the race was a (matrimonial) tie.' But I had no such intention. The puzzle is an arithmetical one, as it purports to be."

(In reply to Solution (of the simple-minded type) by Monika)

An interesting new twist.

However, your calculation actually makes an implicit assumption.  That the gardener can make 33 bounds, then his next bound is 1/3 (1ft) in the direction towards the 100ft. mark, and then 2/3 (2 ft.) and the returning direction.  This requires an instantaniously reversal of direction (ar a similar delay for both - which is stated).  So, besides assuming partial bounds, you are also assuming that a fractional bound uses that same fraction of time as a "full" bound.

If the race were all in one direction, I would not argue so much

Also, the signifcance of All Fool's Day is still not adequately explained, I fear, by anyone, so far (including me!).  The puzzle was both published and ALSO references All Fool's day.  And remember the category is "tricks".

I also think that the ealier "hint" from goFish is a red herring (pun intended).  I looked up the original puzzle where he stated, (only to see how it was phrased), and it consists entirely of paragraph 2.  No other text.  So the intent of the orginal publication should be viewed that way.

Posted by Kenny M on 2006-03-04 13:12:01