Our “Rogers Traveler” from last weekfor his move from Oklahoma to California to increase the intellectual average in both states, it cannot be just any one: it has to be below the average of the first and above the average of the second. With which the joke, implicitly and maliciously, comes to say that a “dumb” (individual below the intellectual average) in Oklahoma is a “smart” (individual above the intellectual average) in California (in which To the extent this joke could have to do with some historical dispute between both states, it is something I do not know).
And speaking of intellectual averagein this thoughtful section the idiot box is not usually mentioned; but two regular commentators agreed, last week, in referring to two television programs that gave them something to think about. Let’s celebrate it as it deserves:
In relation to the issue of the transmission of surnames (incidentally, no one has yet given any answers to the demographic questions raised in the previous installment, so they remain pending), says Bretos Bursó:
“Speaking of the transmission of surnames: this week it came out in The Revolt a man named Christopher Columbus who is a direct descendant (going back 20 generations no less) of the illustrious navigator. It seems to me that few people realize that the vast majority of living descendants of Columbus will neither carry that last name nor know that they are one. What’s more, I this question occurred: What is the probability that among the audience present at the program there were more descendants of Columbus? I’d swear it’s not small. A related question: How many 20-generation ancestors could we estimate that any given person has?”
The lineage of Neem
For his part, Ignacio Alonso comments:
“Last week in The Anthilltwo players, 15 sticks in three rows of 3, 5 and 7 sticks. Taking turns, each player removes the chopsticks they want from a row of their choice. The player who removes the last toothpick from the table loses. What would be the strategy, and for which player, to ensure victory?”
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This is Nim, an ancient game, probably of Chinese origin (like almost everything), which we have dealt with at some time and of which there are numerous variants. For example, you can add a fourth row with a single toothpick:
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In the cult movie Last year in Marienbad (Alain Resnais, 1961) a variant is played, if I remember correctly, in which only a maximum of three sticks can be removed, always from the same row, so the strategy varies slightly (or not?).
The simplest version of this game consists of starting with a single row of 20 toothpicks and taking turns removing one, two or three. The one who takes the last toothpick loses. In this case it is easy to discover the winning strategy; you can start with this trivial single-row Nim and then tackle the other variantssomewhat more complex.
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The Danish poet, engineer and inventor Piet Hein, creator, among other things, of the Soma cube and the Hex board game (and whose ingenious puzzles we have dealt with on more than one occasion, although less than they deserve), devised a interesting “two-dimensional” variant of Nim called Tac Tix, which starts with 16 tiles arranged in a 4×4 grid and tiles can be removed from both rows and columns. But that’s another article.
