Tag Archives: binary numbers

Cat and Mouse

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This is a classic puzzle from Boris Kordemsky’s 1972 Moscow Puzzles.

“Purrer has decided to take a nap.  He dreams he is encircled by 13 mice: 12 gray and 1 white.  He hears his owner saying: “Purrer, you are to eat each thirteenth mouse, keeping the same direction.  The last mouse you eat must be the white one.”  Which mouse should he start from [eat first]?”

Answer.

See Cat and Mouse for a solution.

The Josephus Problem

This famous Josephus Problem presented on Youtube is somewhat different from the Cat and Mice puzzle, but still has similarities.  An article by Jay Bennett discussing the problem was published in Popular Mechanics in 2016.

 

Penn and Teller – Spelling Cards

It turns out that Penn and Teller have performed another magic trick recently that is based on mathematical principles and so is more or less self-working.  It is a more complicated version of the Cat and Mice puzzle, which I have dubbed the “Spelling Cards” trick. Continue reading →

The Weight Problem of Bachet de Méziriac

The following is a famous problem of Bachet as recounted by Heinrich Dörrie in his book 100 Great Problems of Elementary Mathematics:

“A merchant had a forty-pound measuring weight that broke into four pieces as the result of a fall. When the pieces were subsequently weighed, it was found that the weight of each piece was a whole number of pounds and that the four pieces could be used [in a balance scale] to weigh every integral weight between 1 and 40 pounds [when we are allowed to put a weight in either of the two pans]. What were the weights of the pieces?

(This problem stems from the French mathematician Claude Gaspard Bachet de Méziriac (1581-1638), who solved it in his famous book Problèmes plaisants et délectables qui se font par les nombres, published in 1624.)”

The problem has a nice solution using ternary numbers.

Answer.

See the Weight Problem of Bachet for a solution.

(Update 4/10/2019) Continue reading →