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."

First. There is a third character in the race. Consider the character "I" in the narrative. The character knows that the gardener ran 3 feet and the cook ran 2 feet.  How would that be possible if the person was standing at a fixed location? (Speeds may not be easy to estimate) The character "I" could have been the one who won after all.

Next. Consider the possibility that the cook is in the kitchen and the gardener is in the garden, running to a point 100 feet away from the house. It becomes pretty obvious that the gardener will win, since the gardener is unhindered by walls. Nowhere in the riddle was it stated that they started at the same location.

Next. Consider the possibility that the cook is the only existent character, hence the cook wins by default. What exactly is a gardener doing in a country-house...

Next. Consider the possibility that the cook "making" three "bounds" could be in the sense of cooking some sort of food, so only the gardener ran, hence the gardener won.

Last. This is the only one with any arithmetic involved. The cook runs 206 feet in total. This is due to the possibility that you have to cross the 100 feet point before turning in order for it to be considered a valid turn, and you have to cross the finish line, not just touch it. This takes 103 bounds. Assuming 3 bounds are made per unit time, the cook runs for 34.33 units of time. The gardener runs 207 feet in total, for the same reason as stated above. This takes 69 bounds. Assuming 2 bounds are made per unit time, this takes 34.5 units of time.

Based on this measurement, the cook still wins, but by a much smaller margin.

Posted by Jack Lim on 2006-03-02 09:36:42